Elements of operator theory
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2001
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Kubrusly, Carlos S. |d 1947- |e Verfasser |0 (DE-588)173093426 |4 aut | |
| 245 | 1 | 0 | |a Elements of operator theory |c Carlos S. Kubrusly |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XIII, 527 S. | ||
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Datensatz im Suchindex
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| adam_text | CARLOS S. KUBRUSLY ELEMENTS OF OPERATOR THEORY BIRKHAUSER BOSTON * BASEL
* BERLIN CONTENTS PREFACE VII 1 SET-THEORETIC STRUCTURES 1 1.1
BACKGROUND 1 1.2 SETS AND RELATIONS 3 1.3 FUNCTIONS 5 1.4 EQUIVALENCE
RELATIONS 7 1.5 ORDERING 8 1.6 LATTICES 10 1.7 INDEXING 12 1.8
CARDINALITY 14 1.9 REMARKS 21 PROBLEMS 24 2 ALGEBRAIC STRUCTURES 37 2.1
LINEAR SPACES 37 2.2 LINEAR MANIFOLDS 43 2.3 LINEAR INDEPENDENCE 46 2.4
HAMEL BASIS 48 2.5 LINEAR TRANSFORMATIONS 55 2.6 ISOMORPHISMS 58 2.7
ISOMORPHIC EQUIVALENCE 64 2.8 DIRECT SUM 66 XII CONTENTS 2.9 PROJECTIONS
70 PROBLEMS 75 3 TOPOLOGICAL STRUCTURES 85 3.1 METRIC SPACES 85 3.2
CONVERGENCE AND CONTINUITY 93 3.3 OPEN SETS AND TOPOLOGY 100 3.4
EQUIVALENT METRICS AND HOMEOMORPHISMS 106 3.5 CLOSED SETS AND CLOSURE
113 3.6 DENSE SETS AND SEPARABLE SPACES 119 3.7 COMPLETE SPACES 127 3.8
CONTINUOUS EXTENSION AND COMPLETION 134 3.9 THE BAIRE CATEGORY THEOREM
142 3.10 COMPACT SETS 148 3.11 SEQUENTIAL COMPACTNESS 155 PROBLEMS 163 4
BANACH SPACES 197 4.1 NORMED SPACES 197 4.2 EXAMPLES 202 4.3 SUBSPACES
AND QUOTIENT SPACES 209 4.4 BOUNDED LINEAR TRANSFORMATIONS 215 4.5 THE
OPEN MAPPING THEOREM AND CONTINUOUS INVERSES 223 4.6 EQUIVALENCE AND
FINITE-DIMENSIONAL SPACES 230 4.7 CONTINUOUS LINEAR EXTENSION AND
COMPLETION 237 4.8 THE BANACH-STEINHAUS THEOREM AND OPERATOR CONVERGENCE
. . . 242 4.9 COMPACT OPERATORS 250 4.10 THE HAHN-BANACH THEOREM AND
DUAL SPACES 258 PROBLEMS 269 5 HILBERT SPACES 311 5.1 INNER PRODUCT
SPACES 311 5.2 EXAMPLES 318 5.3 ORTHOGONALITY 323 5.4 ORTHOGONAL
COMPLEMENT 328 5.5 ORTHOGONAL STRUCTURE . 335 5.6 UNITARY EQUIVALENCE
339 5.7 SUMMABILITY 343 5.8 ORTHONORMAL BASIS 352 5.9 THE FOURIER SERIES
THEOREM 359 5.10 ORTHOGONAL PROJECTION 367 5.11 THE RIESZ REPRESENTATION
THEOREM AND WEAK CONVERGENCE . . . . 376 5.12 THE ADJOINT OPERATOR 387
5.13 SELF-ADJOINT OPERATORS 396 CONTENTS XIII 5.14 SQUARE ROOT AND POLAR
DECOMPOSITION 401 PROBLEMS 408 6 THE SPECTRAL THEOREM 441 6.1 NORMAL
OPERATORS 441 6.2 THE SPECTRUM OF AN OPERATOR 449 6.3 SPECTRAL RADIUS
457 6.4 NUMERICAL RADIUS 462 6.5 EXAMPLES OF SPECTRA 466 6.6 THE
SPECTRUM OF A COMPACT OPERATOR 474 6.7 THE SPECTRAL THEOREM FOR COMPACT
NORMAL OPERATORS 480 6.8 A GLIMPSE AT THE SPECTRAL THEOREM FOR NORMAL
OPERATORS 489 PROBLEMS 496 REFERENCES 509 INDEX 517
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| any_adam_object | 1 |
| author | Kubrusly, Carlos S. 1947- |
| author_GND | (DE-588)173093426 |
| author_facet | Kubrusly, Carlos S. 1947- |
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| author_sort | Kubrusly, Carlos S. 1947- |
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| bvnumber | BV013884711 |
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| classification_tum | MAT 470f |
| ctrlnum | (OCoLC)45743352 (DE-599)BVBBV013884711 |
| dewey-full | 515/.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.724 |
| dewey-search | 515/.724 |
| dewey-sort | 3515 3724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013884711 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T15:43:21Z |
| institution | BVB |
| isbn | 3764341742 0817641742 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009499139 |
| oclc_num | 45743352 |
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| owner_facet | DE-703 DE-824 DE-20 DE-91 DE-BY-TUM DE-634 DE-83 DE-11 DE-188 |
| physical | XIII, 527 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Kubrusly, Carlos S. 1947- Elements of operator theory Opérateurs, Théorie des Operator theory Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Elements of operator theory |
| title_auth | Elements of operator theory |
| title_exact_search | Elements of operator theory |
| title_full | Elements of operator theory Carlos S. Kubrusly |
| title_fullStr | Elements of operator theory Carlos S. Kubrusly |
| title_full_unstemmed | Elements of operator theory Carlos S. Kubrusly |
| title_short | Elements of operator theory |
| title_sort | elements of operator theory |
| topic | Opérateurs, Théorie des Operator theory Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Opérateurs, Théorie des Operator theory Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009499139&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kubruslycarloss elementsofoperatortheory |