Equations in linear spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Polish Scient. Publ.
1968
|
| Series: | Monografie matematyczne
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 361 - 370. - Aus d. Poln. übers. |
| Physical Description: | 380 S. Ill. |
Staff View
MARC
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| 245 | 1 | 0 | |a Equations in linear spaces |c Danuta Przeworska-Rolewicz and Stefan Rolewicz |
| 264 | 1 | |a Warszawa |b Polish Scient. Publ. |c 1968 | |
| 300 | |a 380 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Monografie matematyczne |v 47 | |
| 500 | |a Literaturverz. S. 361 - 370. - Aus d. Poln. übers. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface 5
Acknowledgment 7
Part A
LINEAR OPERATORS IN LINEAR SPACES
§ 0. Auxiliary notions 15
chapter I
Operators with a finite and semifinite dimensional characteristic
§ 1. Linear operators 25
§ 2. Dimensional characteristic of linear operators 29
§ 3. Finite dimensional operators 33
§ 4. Perturbations of operators 38
§ 5. Algebras of operators and regularization to an ideal 40
§ 6. Quasi Fredholm ideals 42
§ 7. Decomposition of operators 46
§ 8. Eigenvalues, regular values, and the spectrum of an operator 49
§ 9. Pararings and paraalgebras 51
§ 10. Paraalgebras of operators 56
§ 11. Semi Fredholm ideals. Perturbations by means of operators belonging to
some ideals 59
CHAPTER II
Algebraic and almost algebraic operators
§ 1. Hermite s interpolation formula. Partition of unity 65
§ 2. Algebraic and almost algebraic elements in a linear ring 68
§ 3. Properties of polynomials in algebraic and almoRt algebraic elements. . . 71
§ 4. Regularization of polynomials in algebraic and almost algebraic elements 76
§ 5. Algebraic and almost algebraic operators 81
§ 6. Dimensional characteristic of polynomials in algebraic and almost algebraic
operators 84
§ 7. Polynomials in algebraic operators with constant coefficients 85
10 Contents
CHAPTER III
0S operators
§ 1. Conjugate spaces and conjugate operators 90
§ 2. dH characteristic and Pfj operators 94
§3. (S, H) quasi Fredholm ideals 97
§ 4. Perturbations of 0s operators 99
§ 5. Theorems on reduction of the space of functionals 100
CHAPTER IV
Determinant theory Of Pg operators
§ 1. Almost inverse operators. 102
§ 2. Determinant system of a € 3 operator 103
§ 3. Connection between the determinant system and the solutions of equations 107
Part B
LINEAR OPERATORS IN LINEAR TOPOLOGICAL SPACES
CHAPTER I
Linear topological and linear metric spaces
§ 1. Topological spaces and metric spaces 115
§ 2. Properties of linear topological spaces and linear metric spaces 120
§ 3. Examples of linear metric spaces 123
§ 4. Complete linear topological spaces 131
§ 5. Complete linear metric spaces 132
§ 6. Completeness of some linear metric spaces 136
§ 7. Bounded sets and locally bounded spaces 140
§ 8. Convex sets and continuous linear functionals 142
§ 9. Locally convex spaces 147
§ 10. S topology and E convergence 150
§ 11. Riemann integral in complete linear metric spaces 152
CHAPTER II
Continuous linear operators in linear topological spaces
§ 1. Continuous linear operators 157
§ 2. Equicontinuous operators 163
§ 3. Continuity of the inverse of a continuous operator in complete linear metric
spares 165
§ 4. Locally algebraic operators 167
§ 5. Basis of a linear metric space and its properties 168
§ 6. Examples of bases in linear metric spaces 174
§ 7. Continuous operators in spaces with a basis 179
Contents 11
CHAPTER HI
0 operators in linear topological spaces
§ 1. Closed operators 182
§ 2. 0 operators 184
§ 3. Operators conjugate to 0 operators 187
CHAPTER IV
Compact operators in linear topological spaces
§ 1. Compact and precompact sets 189
§ 2. Characterization of precompact sets in concrete spaces 193
§ 3. Compact operators 196
§ 4. Properties of compact operators which map a space into itself 201
§ 5. The Riesz theory 203
§ 6. The set of eigenvalues of a compact operator 207
Part C
LINEAR OPERATORS IN BANACH SPACES
CHAPTER I
Banach spaces
§ 1. Definition of a Banach space 210
§ 2. Continuous operators and continuous functionals in Banach spaces ... 211
§ 3. Weak convergence and weak topology 215
§ 4. Bases in Banach spaces 218
§ 5. Unconditional convergence and unconditional bases 220
§ 6. Linear dimension 223
§ 7. Projections in Banach spaces 226
§ 8. Universality of the space O[0, 1] 232
§ 9. Separable Banach space as a continuous image of the space 1 236
CHAPTER II
Paraalgebras of operators over Banach spaces
§ 1. Fundamental properties of Banach algebras and paraalgebras 238
§ 2. Compact operators 242
§ 3. The ideal of compact operators over Banach spaces containing I . . . . 244
§ 4. Weakly compact operators 249
§ 5. Semicompact operators 252
§ 6. Co semicompact operators 257
§ 7. Spaces with the Dunford Pettis property 263
§ 8. Semicompact and co semicompact operators in the space C(Q) 267
§ 9. Semicompact and co semicompact operators in the space L(Q, E, /i) . . . 271
12 Contents
CHAPTER III
/^ operators in Banach spaces
§ 1. Application of Neumann s series to the solution of equations 275
§ 2. Continuity of solutions 278
§ 3. Normally resolvable operators 281
§ 4. Perturbations with a small norm 283
§ 5. Improved estimations of the norms of small perturbations 291
§ 6. Characterization of the index 293
§ 7. Operators preserving the conjugate space 295
CHAPTER IV
0 points and the theorem on spectral decomposition
§ 1. ^ points 298
§ 2. Properties of functions aA_iI and ^a u 299
§ 3. Analytic functions of operators 302
§ 4. Kesolvent of an operator. A theorem on spectral decomposition 303
§ 5. Decomposition of the operator Pr 306
§ 6. Perturbations of the operator Pr 309
CHAPTER V
Perturbations of E +~, + and 3 operators
§ 1. 0+ ,0_ and 0 perturbations 311
§ 2. The form of the maximal Fredholm ideal in some concrete spaces. . . . 313
§3. Semicompact and co semicompact operators as Z + and / _ perturbations 315
Part D
EXAMPLES OF APPLICATIONS
CHAPTER I
Fredholm Alternative
§ 1. Compactness of integral operators in the space O(Q) 319
§ 2. Fredholm Alternative and an application of the first theorem on the reduction
of functionals 322
§ 3. Weakly singular integral equations 325
§ 4. Integral equations with an integrable kernel. An application of the theorem
on simultaneous approximation 327
§ 5. An application of the Leary WilKamson theorem. Integral equations on the
straight line 328
CHAPTER II
Singular integral equations
§ 1. Cauchy s singular integral and its fundamental properties 331
§ 2. Involutional cases of singular integral equations 335
§ 3. Conjugate operators to singular integral operators 337
Contents 13
§ 4. Index of a singular integral operator 340
§ 5. Systems of singular integral equations 342
§ 6. Almost involutionary cases of singular integral equations 344
§ 7. Singular integral equations with a cotangent kernel 347
CHAPTER III
Operator equations with the Fourier transform and similar transforms
§ 1. Operator equations with the Fourier transform 350
§ 2. Integral transforms with a sinus kernel, a cosinus kernel and a Hankel kernel 352
APPENDIX. Holder and Minkowski inequalities 355
Bibliographical remarks 357
Bibliography 361
List of symbols 371
Subject index 373
Author index 379
|
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| indexdate | 2024-07-09T16:33:16Z |
| institution | BVB |
| language | English |
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| oclc_num | 630251982 |
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| owner | DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-20 DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | 380 S. Ill. |
| psigel | HUB-ZB011201102 |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Polish Scient. Publ. |
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| series | Monografie matematyczne |
| series2 | Monografie matematyczne |
| spelling | Przeworska-Rolewicz, Danuta Verfasser aut Equations in linear spaces Danuta Przeworska-Rolewicz and Stefan Rolewicz Warszawa Polish Scient. Publ. 1968 380 S. Ill. txt rdacontent n rdamedia nc rdacarrier Monografie matematyczne 47 Literaturverz. S. 361 - 370. - Aus d. Poln. übers. Funktionalgleichung (DE-588)4018923-5 gnd rswk-swf Funktionalgleichung (DE-588)4018923-5 s DE-604 Rolewicz, Stefan Verfasser aut Monografie matematyczne 47 (DE-604)BV000003532 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003557610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Przeworska-Rolewicz, Danuta Rolewicz, Stefan Equations in linear spaces Monografie matematyczne Funktionalgleichung (DE-588)4018923-5 gnd |
| subject_GND | (DE-588)4018923-5 |
| title | Equations in linear spaces |
| title_auth | Equations in linear spaces |
| title_exact_search | Equations in linear spaces |
| title_full | Equations in linear spaces Danuta Przeworska-Rolewicz and Stefan Rolewicz |
| title_fullStr | Equations in linear spaces Danuta Przeworska-Rolewicz and Stefan Rolewicz |
| title_full_unstemmed | Equations in linear spaces Danuta Przeworska-Rolewicz and Stefan Rolewicz |
| title_short | Equations in linear spaces |
| title_sort | equations in linear spaces |
| topic | Funktionalgleichung (DE-588)4018923-5 gnd |
| topic_facet | Funktionalgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003557610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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