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Conway J.B. — A Course in Functional Analysis
Conway J.B. — A Course  in Functional Analysis



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Название: A Course in Functional Analysis

Автор: Conway J.B.

Аннотация:

This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 404

Добавлена в каталог: 01.04.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Probabilify measure      84 151
Product of normed spaces      74
Projection      10 37
Proximinal      137
PUB      98
Pythagorean Theorem      7
Quotient map      376
Quotient space      73 131 376
Radical      225
Radon — Nikodym derivative      386
Radon — Nikodym theorem      386
Range of an operator      376
Rapidly decreasing function      342
Rational generator set      227
Real part of an operator      34
Reducing subspace      39
Reductive operator      297
Reflexive operator      298
Reflexive space      92 135
Regular Borel measure      387
Representation      254
Resolvent      203
Resolvent identity      203
Resolvent set      199 314
Restriction of an operator      40
retract      152
Retraction      71 153
Riemann — Lebesgue lemma      22
Riesz functional calculus      206 272
Riesz representation theorem      12 78 389
Right essential spectrum      355
Right Fredholm operator      356
Right ideal      195
Right invertible      195
Right modular ideal      198
Right modular unit      198
Right resolvent set      199
Right spectrum      199
Runge's theorem      86
Ryll — Nardzewski Fixed Point Theorem      157
S      107
Scalar-valued spectral measure      293
Schauder fixed point theorem      154
Schauder's theorem      178
Schur test      30
Schwartz space      343
Second dual      92
Self-adjoint      33 316
Semi-Fredholm operator      356
Semi-inner product      1
Seminorm      65 103
Semisimple      228
Separate points      149
Separated      113
Separating vector      288
Sesquilinear form      31
Signed measure      384
Simple compact normal operator      63
Simple curve      204
Simultaneous diagonalization      273
Simultaneous extension      98
Smaller topology      3 80
SOT      262 281 284
Spatially isomorphic      288
Spectral decomposition      270
Spectral mapping theorem      208 245 296
Spectral measure      262 270
Spectral measure, scalar-valued      293
Spectral picture      374
Spectral radius      201
Spectral Theorem for compact normal operators      56
Spectral Theorem for compact self-adjoint operators      47 50
Spectral theorem for normal operators      269 330
Spectrum      199 314
Star-cyclic      275 277 333
State      256
State space      258
Stone — Cech compactification      141 142 245
Stone — Weierstrass theorem      149
Stone's theorem      337
Stonean space      245 292
Strict inductive limit      122
Strict topology      108 111 119
Strictly separated      113
Strong operator topology      262 281 284
Stronger topology      380
Strongly continuous group      336
Sturm — Liouville operator      51
Sturm — Liouville system      51
Sublinear functional      80 111
Subordinate to a cover      143
Support      69 120
Surjective      376
Symbol      28
Symmetric operator      316
Topological group      159
Topological semigroup      159
Topological vector space      102
Topologically complementary      11 97 125
Totally disconnected      148
Trace      274
Trace norm      274
Trace-class operator      274
Translation invariant      109
Trigonometric polynomial      21
TVs      102
U-compact      70 109
Unconditional convergence      19
Uniform algebra      150
Unilateral shift      29 33 203 214 287 355 360 362 370 371
Unitarily equivalent      61 62 269 299 308
Unitary      20 239
Vanish infinity      67
Variation of a measure      385
Volterra integral operator      216
Volterra kernel      216
Volterra operator      29 45 183 216
von Neumann algebra      288
Weak operator topology      262 281 284
Weak topology      104 127
Weak-star (weak* or wk*) topology      104 128
Weaker topology      380
Weakly Cauchy sequence      136 190
Weakly compact operator      187
Weakly compactly generated      190
Weakly sequentially complete      190
wedge      89
Weighted shift      250 315
Weyl spectrum      373
Winding number      203
WOT      262 281 284
wronskian      52
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