Introduction to functional analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1980
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 467 S. |
| ISBN: | 0471846465 |
Staff View
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Record in the Search Index
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| adam_text | INTRODUCTION TO FUNCTIONAL ANALYSIS SECOND EDITION ANGUS E. TAYLOR
UNIVERSITY OF CALIFORNIA, BERKELEY AND LOS ANGELES DAVID C. LAY
UNIVERSITY OF MARYLAND COLLEGE PARK JOHN WILEY & SONS NEW YORK
CHICHESTER BRISBANE TORONTO CONTENTS INTRODUCTION 1 I THE ABSTRACT
APPROACH TO LINEAR PROBLEMS 4 1.1 ABSTRACT LINEAR SPACES 5 1.2 EXAMPLES
OF LINEAR SPACES 10 1.3 LINEAR OPERATORS 13 1.4 LINEAR OPERATORS IN
FINITE-DIMENSIONAL SPACES 18 1.5 OTHER EXAMPLES OF LINEAR OPERATORS 21
1.6 DIRECT SUMS AND QUOTIENT SPACES 28 1.7 LINEAR FUNCTIONALS 31 1.8
LINEAR FUNCTIONALS IN FINITE-DIMENSIONAL SPACES 35 1.9 ZORN S LEMMA 37
1.10 EXTENSION THEOREMS FOR LINEAR OPERATORS 38 1.11 HAMEL BASES 41 1.12
THE TRANSPOSE OF A LINEAR OPERATOR 44 1.13 ANNIHILATORS, RANGES, AND
NULL SPACES 45 1.14 CONCLUSIONS 49 II TOPOLOGICAL LINEAR SPACES 51 II. 1
NORMED LINEAR SPACES 52 11.2 EXAMPLES OF NORMED LINEAR SPACES 56 11.3
FINITE-DIMENSIONAL NORMED LINEAR SPACES 62 11.4 BANACH SPACES 66 11.5
QUOTIENT SPACES 71 11.6 INNER-PRODUCT SPACES 73 11.7 HILBERT SPACE 86
11.8 EXAMPLES OF COMPLETE ORTHONORMAL SETS 91 11.9 TOPOLOGICAL LINEAR
SPACES 94 11.10 CONVEX SETS 100 11.11 LOCALLY CONVEX SPACES 105 11.12
MINKOWSKI FUNCTIONALS 111 11.13 METRIZABLE TOPOLOGICAL LINEAR SPACES 115
III LINEAR FUNCTIONALS AND WEAK TOPOLOGIES 121 111.1 LINEAR VARIETIES
AND HYPERPLANES 122 111.2 THE HAHN-BANACH THEOREM 125 111.3 THE
CONJUGATE OF A NORMED LINEAR SPACE 134 IX X CONTENTS 111.4 THE SECOND
CONJUGATE SPACE 139 111.5 SOME REPRESENTATIONS OF LINEAR FUNCTIONALS 141
111.6 WEAK TOPOLOGIES FOR LINEAR SPACES 156 111.7 POLAR SETS AND
ANNIHILATORS 160 111.8 EQUICONTINUITY AND -TOPOLOGIES 165 111.9 THE
PRINCIPLE OF UNIFORM BOUNDEDNESS 169 111.10 WEAK TOPOLOGIES FOR NORMED
LINEAR SPACES 172 111.11 THE KREIN-MILMAN THEOREM 181 IV GENERAL
THEOREMS ON LINEAR OPERATORS 188 IV. 1 SPACES OF LINEAR OPERATORS 189
IV.2 INTEGRAL EQUATIONS OF THE SECOND KIND 196 IV.3 ^KERNELS 201 IV.4
DIFFERENTIAL EQUATIONS AND INTEGRAL EQUATIONS 205 IV.5 CLOSED LINEAR
OPERATORS 208 IV.6 SOME REPRESENTATIONS OF BOUNDED LINEAR OPERATORS 219
IV.7 THE M. RIESZ CONVEXITY THEOREM 224 IV.8 CONJUGATES OF LINEAR
OPERATORS 226 IV.9 THEOREMS ABOUT CONTINUOUS INVERSES 234 IV. 10 THE
STATES OF AN OPERATOR AND ITS CONJUGATE 237 IV. 11 ADJOINT OPERATORS 242
IV. 12 PROJECTIONS 246 IV. 13 FREDHOLM OPERATORS 253 V SPECTRAL ANALYSIS
OF LINEAR OPERATORS 264 V.I ANALYTIC VECTOR-VALUED FUNCTIONS 265 V.2 THE
RESOLVENT OPERATOR 272 V.3 THE SPECTRUM OF A BOUNDED LINEAR OPERATOR 277
V.4 SUBDIVISIONS OF THE SPECTRUM 282 V.5 REDUCIBILITY 287 V.6 THE ASCENT
AND DESCENT OF AN OPERATOR 289 V.7 COMPACT OPERATORS 293 V.8 AN
OPERATIONAL CALCULUS 309 V.9 SPECTRAL SETS. THE SPECTRAL MAPPING THEOREM
320 V.10 ISOLATED POINTS OF THE SPECTRUM 328 V.LL OPERATORS WITH A
RATIONAL RESOLVENT 336 VI SPECTRAL ANALYSIS IN HILBERT SPACE 341, VI. 1
BILINEAR AND QUADRATIC FORMS 342 VI.2 SYMMETRIC OPERATORS 345 VI.3
NORMAL AND SELF-ADJOINT OPERATORS 349 VI.4 COMPACT SYMMETRIC OPERATORS
353 VI.5 SYMMETRIC OPERATORS WITH COMPACT RESOLVENT 361 VI.6 THE
SPECTRAL THEOREM FOR BOUNDED SELF-ADJOINT OPERATORS 363 VI.7 UNITARY
OPERATORS 374 VI.8 UNBOUNDED SELF-ADJOINT OPERATORS 380 CONTENTS XI VII
BANACH ALGEBRAS 386 VII. 1 EXAMPLES OF BANACH ALGEBRAS 387 VII.2
SPECTRAL THEORY IN A BANACH ALGEBRA 393 VII.3 IDEALS AND HOMOMORPHISMS
400 VI1.4 COMMUTATIVE BANACH ALGEBRAS 404 VII.5 APPLICATIONS AND
EXTENSIONS OF THE GELFAND THEORY 415 VII.6 *-ALGEBRAS 426 VI1.7 THE
SPECTRAL THEOREM FOR A NORMAL OPERATOR 430 BIBLIOGRAPHY 445 LIST OF
SPECIAL SYMBOLS 455 INDEX 459
|
| any_adam_object | 1 |
| author | Taylor, Angus E. 1911-1999 Lay, David C. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-search | QA320 |
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| ctrlnum | (OCoLC)4983066 (DE-599)BVBBV002265773 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:02Z |
| institution | BVB |
| isbn | 0471846465 |
| language | English |
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| physical | XI, 467 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Wiley |
| record_format | marc |
| spelling | Taylor, Angus E. 1911-1999 Verfasser (DE-588)1013619420 aut Introduction to functional analysis Angus E. Taylor ; David C. Lay 2. ed. New York [u.a.] Wiley 1980 XI, 467 S. txt rdacontent n rdamedia nc rdacarrier Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Lay, David C. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001488915&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, Angus E. 1911-1999 Lay, David C. Introduction to functional analysis Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4151278-9 |
| title | Introduction to functional analysis |
| title_auth | Introduction to functional analysis |
| title_exact_search | Introduction to functional analysis |
| title_full | Introduction to functional analysis Angus E. Taylor ; David C. Lay |
| title_fullStr | Introduction to functional analysis Angus E. Taylor ; David C. Lay |
| title_full_unstemmed | Introduction to functional analysis Angus E. Taylor ; David C. Lay |
| title_short | Introduction to functional analysis |
| title_sort | introduction to functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Einführung |
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