Normed algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German English |
| Veröffentlicht: |
Groningen
Wolters-Noordhoff
1972
|
| Ausgabe: | 3., compl. rev. Americal ed. of "Normed Rings", transl. from the second Russian ed., publ. 1968, Moscow |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 598 S. |
| ISBN: | 9001614752 |
Internformat
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| 100 | 1 | |a Najmark, Mark A. |d 1909-1978 |e Verfasser |0 (DE-588)1026635349 |4 aut | |
| 240 | 1 | 0 | |a Normirovannye kol'ca |
| 245 | 1 | 0 | |a Normed algebras |c M. A. Naimark |
| 250 | |a 3., compl. rev. Americal ed. of "Normed Rings", transl. from the second Russian ed., publ. 1968, Moscow | ||
| 264 | 1 | |a Groningen |b Wolters-Noordhoff |c 1972 | |
| 300 | |a XVI, 598 S. | ||
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Datensatz im Suchindex
| _version_ | 1804117023691636737 |
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| adam_text | NORMED ALGEBRAS BY M. A. NAIMARK STEKLOV INSTITUTE OF MATHEMATICS,
ACADEMY OF SCIENCES, U.S.S.R. TRANSLATED FROM THE SECOND RUSSIAN EDITION
BY LEO F. BORON UNIVERSITY OF IDAHO, MOSCOW, U.S.A. FACHBEREICH M
ARBEITSGRU TECHNISCHE HE DARMST ATTSGESONDERT PE 5 DARMSTADT 9
WOLTERS-NOORDHOFF PUBLISHING GRONINGEN THE NETHERLANDS CONTENTS
DEDICATION V FOREWORD TO THE THIRD AMERICAN EDITION VM FOREWORD TO THE
SECOND (= REVISED FIRST) AMERICAN EDITION VM FOREWORD TO THE SECOND
SOVIET EDITION XIV FROM THE FOREWORD TO THE FIRST SOVIET EDITION XV
CHAPTER I BASIC IDEAS FROM TOPOLOGY AND FUNCTIONAL ANALYSIS § 1. LINEAR
SPACES 1 1. DEFINITION OF A LINEAR SPACE (1). 2. LINEAR DEPENDENCE AND
INDEPENDENCE OF VECTORS (2). 3. SUBSPACES (3). 4. QUOTIENT SPACE (4). 5.
LINEAR OPERATORS (5). 6. OPERATOR CAL- CULUS (8). 7. INVARIANT SUBSPACES
(12). 8. CONVEX SETS AND MINKOWSKI FUNCTIONALS (12). 9. THEOREMS ON THE
EXTENSION OF A LINEAR FUNCTIONAL (16). § 2. TOPOLOGICAL SPACES 21 1.
DEFINITION OF A TOPOLOGICAL SPACE (21). 2. INTERIOR OF A SET;
NEIGHBORHOODS (22). 3. CLOSED SETS; CLOSURE OF A SET (23). 4. SUBSPACES
(24). 5. MAPPINGS OF TOPOLOGICAL SPACES (24). 6. COMPACT SETS (26). 7.
HAUSDORFF SPACES (27). 8. NORMAL SPACES (28). 9. LOCAL- LY COMPACT
SPACES (30). 10. STONE S THEOREM (30). 11. WEAK TOPOLOGY, DEFINED BY A
FAM- ILY OF FUNCTIONS (33). 12. TOPOLOGICAL PRODUCT OF SPACES (34). 13.
METRIC SPACES (36). 14. COMPACT SETS IN METRIC SPACES (41). 15.
TOPOLOGICAL PRODUCT OF METRIC SPACES (42). § 3. TOPOLOGICAL LINEAR
SPACES 44 I. DEFINITION OF A TOPOLOGICAL LINEAR SPACE (44). 2. CLOSED
SUBSPACES IN TOPOLOGICAL LIN- EAR SPACES (46). 3. CONVEX SETS IN LOCALLY
CONVEX SPACES (46). 4. DEFINING A LOCALLY CON- VEX TOPOLOGY IN TERMS OF
SEMINORMS (47). 5. THE CASE OF A FINITE-DIMENSIONAL SPACE (50). 6.
CONTINUOUS LINEAR FUNCTIONALS (52). 7. CONJUGATE SPACE (55). 8. CONVEX
SETS IN A FINITE- DIMENSIONAL SPACE (58). 9. CONVEX SETS IN THE
CONJUGATE SPACE (58). 10. CONES (63). I1. ANNIHILATORS IN THE CONJUGATE
SPACE (64). 12. ANALYTIC VECTOR-VALUED FUNCTIONS (66). 13. COMPLETE
LOCALLY CONVEX SPACES (67). § 4. NORMED SPACES 67 1. DEFINITION OF A
NORMED SPACE (67). 2. SERIES IN A NORMED SPACE (72). 3. QUOTIENT SPACES
OF A BANACH SPACE (73). 4. BOUNDED LINEAR OPERATORS (74). 5. BOUNDED
LINEAR FUNCTIONALS; CONJUGATE SPACE (78). 6. COMPACT (OR COMPLETELY
CONTINUOUS) OPERATORS (79). 7. ANALYTIC VECTOR-VALUED FUNCTIONS IN A
BANACH SPACE (80). § 5. HILBERT SPACE 82 1. DEFINITION OF HILBERT SPACE
(82). 2. PROJECTION OF A VECTOR ON A SUBSPACE (85). 3. BOUNDED LINEAR
FUNCTIONALS IN HILBERT SPACE (88). 4. ORTHOGONAL SYSTEMS OF VECTORS IN
HILBERT SPACE (90). 5. ORTHOGONAL SUM OF SUBSPACES (95). 6. DIREC^SUM OF
HILBERT SPA- CES (96). 7. GRAPH OF AN OPERATOR (97). 8. CLOSED
OPERATORS; CLOSURE OF AN OPERATOR (97). 9. ADJOINT OPERATOR (99). 10.
THE CASE OF A BOUNDED OPERATOR (103). 11. GENERAL- IZATION TO OPERATORS
IN A BANACH SPACE (105). 12. PROJECTION OPERATORS (106). 13. RE-
DUCIBILITY (110). 14. PARTIALLY ISOMETRIC OPERATORS (110). 15. MATRIX
REPRESENTATION OF AN OPERATOR (111). § 6. INTEGRATION ON LOCALLY COMPACT
SPACES 114 1. FUNDAMENTAL CONCEPTS; FORMULATION OF THE PROBLEM (114). 2.
FUNDAMENTAL PROPER- TIES OF THE INTEGRAL (114). 3. EXTENSION OF THE
INTEGRAL TO LOWER SEMI-CONTINUOUS FUNC- TIONS (115). 4. UPPER INTEGRAL
OF AN ARBITRARY NONNEGATIVE REAL-VALUED FUNCTION (118). VII VIII
CONTENTS 5. EXTERIOR MEASURE OF A SET (119). 6. EQUIVALENT FUNCTIONS
(120). 7. THE SPACES JSF 1 ANDL 1 (122). 8. SUMMABLE SETS (125). 9.
MEASURABLE SETS (128). 10. MEASURABLE FUNCTIONS (129). 11. THE REAL
SPACE L 2 (135). 12. THE COMPLEX SPACE L 2 (137). 13. THE SPACE L 00
(137). 14. THE POSITIVE AND NEGATIVE PARTS OF A LINEAR FUNCTIONAL (137).
15. THE RADON-NIKODYM THEOREM (139). 16. THE SPACE CONJUGATE TO L 1
(140). 17. COM- PLEX MEASURES (143). 18. INTEGRALS ON THE DIRECT PRODUCT
OF SPACES (144). 19. THE INTEGRATION OF VECTOR-VALUED AND
OPERATOR-VALUED FUNCTIONS (149). CHAPTER II FUNDAMENTAL CONCEPTS AND
PROPOSITIONS IN THE THEORY OF NORMED ALGEBRAS § 7. FUNDAMENTAL ALGEBRAIC
CONCEPTS 152 1. DEFINITION OF A LINEAR ALGEBRA (152). 2. ALGEBRAS WITH
IDENTITY (153). 3. CENTER (156). 4. IDEALS (156). 5. THE (JACOBSON)
RADICAL (161). 6. HOMOMORPHISM AND ISOMORPHISM OF ALGEBRAS (164). 7.
REGULAR REPRESENTATIONS OF ALGEBRAS (165). § 8. TOPOLOGICAL ALGEBRAS 167
1. DEFINITION OF A TOPOLOGICAL ALGEBRA (167). 2. TOPOLOGICAL ADJUNCTION
OF THE IDENTITY (169). 3. ALGEBRAS WITH CONTINUOUS INVERSE (169). 4.
RESOLVENTS IN AN ALGEBRA WITH CON- TINUOUS INVERSE (171). 5. TOPOLOGICAL
DIVISION ALGEBRAS WITH CONTINUOUS INVERSE (173). 6. ALGEBRAS WITH
CONTINUOUS QUASI-INVERSE (173). § 9. NORMED ALGEBRAS 174 1. DEFINITION
OF A NORMED ALGEBRA (174). 2. ADJUNCTION OF THE IDENTITY (176). 3. THE
RADICAL IN A NORMED ALGEBRA (176). 4. BANACH ALGEBRAS WITH IDENTITY
(177). 5. RESOLVENT IN A BANACH ALGEBRA WITH IDENTITY (179). 6.
CONTINUOUS HOMOMORPHISMS OF NORMED ALGEBRAS (179). 7. REGULAR
REPRESENTATIONS OF A NORMED ALGEBRA (180). § 10. SYMMETRIC ALGEBRAS 183
1. DEFINITION AND SIMPLEST PROPERTIES OF A SYMMETRIC ALGEBRA (183). 2.
POSITIVE FUNC- TIONALS (185). 3. NORMED SYMMETRIC ALGEBRAS (187). 4.
POSITIVE FUNCTIONALS IN A SYM- METRIC BANACH ALGEBRA (188). CHAPTER III
COMMUTATIVE NORMED ALGEBRAS § 11. REALIZATION OF A COMMUTATIVE NORMED
ALGEBRA IN THE FORM OF AN ALGEBRA OF FUNCTIONS . . 191 1. QUOTIENT
ALGEBRA MODULO A MAXIMAL IDEAL (191). 2. FUNCTIONS ON MAXIMAL IDEALS
GENERATED BY ELEMENTS OF AN ALGEBRA (192). 3. TOPOLOGIZATION OF THE SET
OF ALL MAXIMAL IDEALS (195). 4. THE CASE OF AN ALGEBRA WITHOUT IDENTITY
(198). 5. SYSTEM OF GENERATORS OF AN ALGEBRA (199). 6. ANALYTIC
FUNCTIONS OF ALGEBRA ELEMENTS (200). 7. WIENER PAIRS OF ALGEBRAS (203).
8. FUNCTIONS OF SEVERAL ALGEBRA ELEMENTS! LOCALLY ANALYTIC FUNCTIONS
(205). 9. DECOMPOSITION OF AN ALGEBRA INTO THE DIRECT SUM OF IDEALS
(207). 10. ALGEBRAS WITH RADICAL (207). § 12. HOMOMORPHISM AND
ISOMORPHISM OF COMMUTATIVE ALGEBRAS 208 1. UNIQUENESS OF THE NORM IN A
SEMISIMPLE ALGEBRA (208). 2. THE CASE OF SYMMETRIC ALGEBRAS (210). § 13.
ALGEBRA (OR SHILOV) BOUNDARY 210 1. DEFINITION AND FUNDAMENTAL
PROPERTIES OF THE ALGEBRA BOUNDARY (210). 2. EXTENSION OF MAXIMAL IDEALS
(212). CONTENTS IX 14. COMPLETELY SYMMETRIC COMMUTATIVE ALGEBRAS 215 1.
DEFINITION OF A COMPLETELY SYMMETRIC ALGEBRA (215). 2. CRITERION FOR
COMPLETE SYM- METRY (215). 3. APPLICATION OF STONE S THEOREM (216). 4.
THE ALGEBRA BOUNDARY OF A COMPLETELY SYMMETRIC ALGEBRA (218). 15.
REGULAR ALGEBRAS 218 1. DEFINITION OF A REGULAR ALGEBRA (218). 2. NORMAL
ALGEBRAS OF FUNCTIONS (219). 3. STRUCTURE SPACE OF AN ALGEBRA (221). 4.
PROPERTIES OF REGULAR ALGEBRAS (222). 5. THE CASE OF AN ALGEBRA WITHOUT
IDENTITY (226). 6. SUFFICIENT CONDITION THAT AN ALGEBRA BE REGULAR
(227). 7. PRIMARY IDEALS (227). 16. COMPLETELY REGULAR COMMUTATIVE
ALGEBRAS 228 1. DEFINITION AND SIMPLEST PROPERTIES OF A COMPLETELY
REGULAR ALGEBRA (228). 2. REALI- ZATION OF COMPLETELY REGULAR
COMMUTATIVE ALGEBRAS (230). 3. GENERALIZATION TO MULTI- NORMED ALGEBRAS
(236). 4. SYMMETRIC SUBALGEBRAS OF THE ALGEBRA C(T) AND COMPACT
EXTENSIONS OF THE SPACE T (237). 5. ANTISYMMETRIC SUBALGEBRAS OF THE
ALGEBRA C(T) (238). 6. SUBALGEBRAS OF THE ALGEBRA C(T) AND CERTAIN
PROBLEMS IN APPROXIMATION THEORY (239). CHAPTER IV REPRESENTATIONS OF
SYMMETRIC ALGEBRAS 17. FUNDAMENTAL CONCEPTS AND PROPOSITIONS IN THE
THEORY OF REPRESENTATIONS 242 1. DEFINITIONS AND SIMPLEST PROPERTIES OF
A REPRESENTATION (242). 2. DIRECT SUM OF RE- PRESENTATIONS (243). 3.
DESCRIPTION OF REPRESENTATIONS IN TERMS OF POSITIVE FUNCTIONALS (244).
4. REPRESENTATIONS OF COMPLETELY REGULAR COMMUTATIVE ALGEBRAS; SPECTRAL
THEO- , REM (248). 5. SPECTRAL OPERATORS (256). 6. IRREDUCIBLE
REPRESENTATIONS (258). 7. CON- NECTION BETWEEN VECTORS AND POSITIVE
FUNCTIONALS (259). 18. EMBEDDING OF A SYMMETRIC ALGEBRA IN AN ALGEBRA OF
OPERATORS 260 1. REGULAR NORM (260). 2. REDUCED ALGEBRAS (261). 3.
MINIMAL REGULAR NORM (264). 19. INDECOMPOSABLE FUNCTIONALS AND
IRREDUCIBLE REPRESENTATIONS 256 1. POSITIVE FUNCTIONALS, DOMINATED BY A
GIVEN POSITIVE FUNCTIONAL (266). 2. THE ALGEBRA C F (269). 3.
INDECOMPOSABLE POSITIVE FUNCTIONALS (270). 4. COMPLETENESS AND APPROXI-
MATION THEOREMS (270). 20. APPLICATION TO COMMUTATIVE SYMMETRIC ALGEBRAS
274 1. MINIMAL REGULAR NORM IN A COMMUTATIVE SYMMETRIC ALGEBRA (274). 2.
POSITIVE FUNC- TIONALS IN A COMMUTATIVE SYMMETRIC ALGEBRA (275). 3.
EXAMPLES (278). 4. THE CASE OF A COMPLETELY SYMMETRIC ALGEBRA (281). 21.
GENERALIZED SCHUR LEMMA 288 1. CANONICAL DECOMPOSITION OF AN OPERATOR
(288). 2. FUNDAMENTAL THEOREM (290). 3. APPLICATION TO DIRECT SUMS OF
PAIRWISE NON-EQUIVALENT REPRESENTATIONS (292). 4. APPLI- CATION TO
REPRESENTATIONS WHICH ARE MULTIPLES OF A GIVEN IRREDUCIBLE
REPRESENTATION (293). 22. SOME REPRESENTATIONS OF THE ALGEBRA S3(JP) 295
1. IDEALS IN THE ALGEBRA S3 (§) (296). 2. THE ALGEBRA I O AND ITS
REPRESENTATIONS (298). 3. REPRESENTATIONS OF THE ALGEBRA 58(§) (300). :
CONTENTS CHAPTER V SOME SPECIAL ALGEBRAS 23. COMPLETELY SYMMETRIC
ALGEFIRAS 303 1 . DEFINITION AND EXAMPLES OF COMPLETELY SYMMETRIC
ALGEBRAS (303). 2. SPECTRUM (304). 3. THEOREMS ON EXTENSIONS (306). 4.
CRITERION FOR COMPLETE SYMMETRY (312). 24. COMPLETELY REGULAR ALGEBRAS
314 1. FUNDAMENTAL PROPERTIES OF COMPLETELY REGULAR ALGEBRAS (314). 2.
REALIZATION OF A COMPLETELY REGULAR ALGEBRA AS AN ALGEBRA OF OPERATORS
(316). 3. QUOTIENT ALGEBRA OF A COMPLETELY REGULAR ALGEBRA (319). 25.
DUAL ALGEBRAS 320 1. ANNIHILATOR ALGEBRAS AND DUAL ALGEBRAS (320). 2.
IDEALS IN AN ANNIHILATOR ALGEBRA (322). 3. SEMISIMPLE ANNIHILATOR
ALGEBRAS (325). 4. SIMPLE ANNIHILATOR ALGEBRAS (330). 5. H*-ALGEBRAS
(334). 6. COMPLETELY REGULAR DUAL ALGEBRAS (336). 26. ALGEBRAS OF
VECTOR-VALUED FUNCTIONS 339 1. DEFINITION OF AN ALGEBRA OF VECTOR-VALUED
FUNCTIONS (339). 2. IDEALS IN AN ALGEBRA OF. VECTOR-VALUED FUNCTIONS
(340). 3. CONDITIONS FOR A VECTOR-VALUED FUNCTION TO BELONG TO AN
ALGEBRA (342). 4. THE CASE OF COMPLETELY REGULAR ALGEBRAS (343). 5.
CONTINUOUS ANALOGUE OF THE SCHUR LEMMA (351). 6. STRUCTURE SPACE OF A
COMPLETELY REGULAR ALGEBRA (358). CHAPTER VI GROUP ALGEBRAS 27.
TOPOLOGICAL GROUPS 361 1. DEFINITION OF A GROUP (361). 2. SUBGROUPS
(362). 3. DEFINITION AND SIMPLEST PROPER- TIES OF A TOPOLOGICAL GROUP
(363). 4. INVARIANT INTEGRALS AND INVARIANT MEASURES ON A LO- CALLY
COMPACT GROUP (364). 5. EXISTENCE OF AN INVARIANT INTEGRAL ON A LOCALLY
COMPACT GROUP (365). 28. DEFINITION AND FUNDAMENTAL PROPERTIES OF A
GROUP ALGEBRA 373 1. DEFINITION OF A GROUP ALGEBRA (373). 2. SOME
PROPERTIES OF THE GROUP ALGEBRA (377). 29. UNITARY REPRESENTATIONS OF A
LOCALLY COMPACT GROUP AND THEIR RELATIONSHIP WITH THE REPRE- SENTATIONS
OF THE GROUP ALGEBRA 380 1. UNITARY REPRESENTATIONS OF A GROUP (380). 2.
RELATIONSHIP BETWEEN REPRESENTATIONS OF A GROUP AND OF THE GROUP ALGEBRA
(381). 3. COMPLETENESS THEOREM (385). 4. EXAMPLES: A) UNITARY
REPRESENTATIONS OF THE GROUP OF LINEAR TRANSFORMATIONS OF THE REAL LINE
(386); B) UNITARY REPRESENTATIONS OF THE PROPER LORENTZ GROUP (387); C)
EXAMPLE OF A GROUP ALGEBRA WHICH IS NOT COMPLETELY SYMMETRIC (393). X?
30. POSITIVE DEFINITE FUNCTIONS 398 1. POSITIVE DEFINITE FUNCTIONS AND
THEIR RELATIONSHIP WITH UNITARY REPRESENTATIONS (398). 2. RELATIONSHIP
OF POSITIVE DEFINITE FUNCTIONS WITH POSITIVE FUNCTIONALS ON A GROUP AL-
GEBRA (400). 3. REGULAR SETS (404). 4. TRIGONOMETRIC POLYNOMIALS ON A
GROUP (407). 5. SPECTRUM (407). 31. HARMONIC ANALYSIS ON COMMUTATIVE
LOCALLY COMPACT GROUPS 410 1. MAXIMAL IDEALS OF THE GROUP ALGEBRA OF A
COMMUTATIVE GROUP; CHARACTERS (410). 2. GROUP OF CHARACTERS (415). 3.
POSITIVE DEFINITE FUNCTIONS ON A COMMUTATIVE GROUP CONTENTS XI (416). 4.
INVERSION FORMULA AND PLANCHEREL S THEOREM FOR COMMUTATIVE GROUPS (418).
5. ^SEPARATION PROPERTY OF THE SET [L 1 N P] (424). 6. DUALITY THEOREM
(424). 7. UNITARY REPRESENTATIONS OF COMMUTATIVE GROUPS (426). 8.
THEOREMS OF TAUBERIAN TYPE (427). 9. THE CASE OF A COMPACT GROUP (432).
10. SPHERICAL FUNCTIONS (433). 11. THE GENERAL- IZED TRANSLATION
OPERATION (435). 32. REPRESENTATIONS OF COMPACT GROUPS 438 1. THE
ALGEBRA L 2 (@) (438). 2. REPRESENTATIONS OF A COMPACT GROUP (439). 3.
TENSOR PRODUCT OF REPRESENTATIONS (445). 4. DUALITY THEOREM FOR A
COMPACT GROUP (446). CHAPTER VII ALGEBRAS OF OPERATORS IN HILBERT SPACE
33. VARIOUS TOPOLOGIES IN THE ALGEBRA S3 (§) 449 1. WEAK TOPOLOGY (449).
2. STRONG TOPOLOGY (449). 3. STRONGEST TOPOLOGY (451). 4. UNI- FORM
TOPOLOGY (452).^ 34. WEAKLY CLOSED SUBALGEBRAS OF THE ALGEBRA S3 (§) 452
1. FUNDAMENTAL CONCEPTS (452). 2. PRINCIPAL IDENTITY (453). 3. CENTER
(457). 4. FACTORI- ZATION (458). 35. RELATIVE EQUIVALENCE 458 1.
OPERATORS AND SUBSPACES ADJOINED TO AN ALGEBRA (458). 2. FUNDAMENTAL
LEMMA (459). 3. DEFINITION OF RELATIVE EQUIVALENCE (460). 4. COMPARISON
OF CLOSED SUBSPACES (460). 5. FINITE AND INFINITE SUBSPACES (463). 36.
RELATIVE DIMENSION 467 1. ENTIRE PART OF THE RATIO OF TWO SUBSPACES
(467). 2. THE CASE WHEN A MINIMAL SUBSPACE EXISTS (468). 3. THE CASE
WHEN A MINIMAL SUBSPACE DOES NOT EXIST (469). 4. EXISTENCE AND
PROPERTIES OF RELATIVE DIMENSION (470). 5. THE RANGE OF THE RELATIVE
DIMENSION; CLASSIFICATION OF FACTORS (475). 6. INVARIANCE OF FACTOR TYPE
UNDER SYMMETRIC ISOMOR- PHISMS (477). 37. RELATIVE TRACE 478 1.
DEFINITION OF TRACE (478). 2. PROPERTIES OF THE TRACE (479). 3. TRACES
IN FACTORS OF TYPES (1^) AND (11^) (484). 38. STRUCTURE AND EXAMPLES OF
SOME TYPES OF FACTORS 484 L.THE MAPPING M-*M (SD1 ) (484). 2. MATRIX
DESCRIPTION OF FACTORS OF TYPES (I) AND (II) (486). 3. DESCRIPTION OF
FACTORS OF TYPE (I) (488). 4. STRUCTURE OFTACTORS OF TYPE (11^) (490).
5. EXAMPLE OF A FACTOR OF TYPE (IIJ) (490). 6. APPROXIMATELY FINITE
FACTORS OF TYPE (HI) (493). 7. RELATIONSHIP BETWEEN THE TYPES OF FACTORS
M AND M (493). 8. RELA- TIONSHIP BETWEEN SYMMETRIC AND SPATIAL
ISOMORPHISMS (494). 9. UNBOUNDED OPERA- TORS, ADJOINED TO A FACTOR OF
FINITE TYPE (494). 39. UNITARY ALGEBRAS AND ALGEBRAS WITH TRACE 494 1.
DEFINITION OF A UNITARY ALGEBRA (494). 2. DEFINITION OF AN ALGEBRA WITH
TRACE (494). 3. UNITARY ALGEBRAS DEFINED BY THE TRACE (495). 4.
CANONICAL TRACE IN A UNITARY ALGEBRA (495). XII CONTENTS CHAPTER VIII
DECOMPOSITION OF AN ALGEBRA OF OPERATORS INTO IRREDUCIBLE ALGEBRAS § 40.
FORMULATION OF THE PROBLEM; CANONICAL FORM OF A COMMUTATIVE ALGEBRA OF
OPERATORS IN HILBERT SPACE 499 1. FORMULATION OF THE PROBLEM (499). 2.
THE SEPARABILITY LEMMA (501). 3. CANONICAL FORM OF A COMMUTATIVE ALGEBRA
(502). § 41. DIRECT INTEGRAL OF HILBERT SPACES; THE DECOMPOSITION OF AN
ALGEBRA OF OPERATORS INTO THE DIRECT INTEGRAL OF IRREDUCIBLE ALGEBRAS
505 1. DIRECT INTEGRAL OF HILBERT SPACES (505). 2. DECOMPOSITION OF A
HILBERT SPACE INTO A DIRECT INTEGRAL WITH RESPECT TO A GIVEN COMMUTATIVE
ALGEBRA R (508). 3. DECOMPOSITION WITH RESPECT TO A MAXIMAL COMMUTATIVE
ALGEBRA; CONDITION FOR IRREDUCIBILITY (513). 4. _ DECOMPOSITION OF A
UNITARY REPRESENTATION OF A LOCALLY COMPACT GROUP INTO IRREDUCIBLE
REPRESENTATIONS (517). 5. CENTRAL DECOMPOSITIONS AND FACTOR
REPRESENTATIONS (521). 6. REPRESENTATIONS IN A SPACE WITH AN INDEFINITE
METRIC (521). APPENDIX I PARTIALLY ORDERED SETS AND ZORN S LEMMA 523
APPENDIX II BOREL SPACES AND BOREL FUNCTIONS 523 APPENDIX III ANALYTIC
SETS 525 LITERATURE 532 INDEX 575
|
| any_adam_object | 1 |
| author | Najmark, Mark A. 1909-1978 |
| author_GND | (DE-588)1026635349 |
| author_facet | Najmark, Mark A. 1909-1978 |
| author_role | aut |
| author_sort | Najmark, Mark A. 1909-1978 |
| author_variant | m a n ma man |
| building | Verbundindex |
| bvnumber | BV002643607 |
| classification_rvk | SK 230 SK 340 SK 600 |
| ctrlnum | (OCoLC)476310286 (DE-599)BVBBV002643607 |
| discipline | Mathematik |
| edition | 3., compl. rev. Americal ed. of "Normed Rings", transl. from the second Russian ed., publ. 1968, Moscow |
| format | Book |
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| id | DE-604.BV002643607 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:49Z |
| institution | BVB |
| isbn | 9001614752 |
| language | German English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001696272 |
| oclc_num | 476310286 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-20 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-20 DE-83 |
| physical | XVI, 598 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Wolters-Noordhoff |
| record_format | marc |
| spelling | Najmark, Mark A. 1909-1978 Verfasser (DE-588)1026635349 aut Normirovannye kol'ca Normed algebras M. A. Naimark 3., compl. rev. Americal ed. of "Normed Rings", transl. from the second Russian ed., publ. 1968, Moscow Groningen Wolters-Noordhoff 1972 XVI, 598 S. txt rdacontent n rdamedia nc rdacarrier Funktionenalgebra (DE-588)4155686-0 gnd rswk-swf Funktionenalgebra (DE-588)4155686-0 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001696272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Najmark, Mark A. 1909-1978 Normed algebras Funktionenalgebra (DE-588)4155686-0 gnd |
| subject_GND | (DE-588)4155686-0 |
| title | Normed algebras |
| title_alt | Normirovannye kol'ca |
| title_auth | Normed algebras |
| title_exact_search | Normed algebras |
| title_full | Normed algebras M. A. Naimark |
| title_fullStr | Normed algebras M. A. Naimark |
| title_full_unstemmed | Normed algebras M. A. Naimark |
| title_short | Normed algebras |
| title_sort | normed algebras |
| topic | Funktionenalgebra (DE-588)4155686-0 gnd |
| topic_facet | Funktionenalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001696272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT najmarkmarka normirovannyekolca AT najmarkmarka normedalgebras |