Ya Helemskii A., West A. — Banach and locally convex algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Ya Helemskii A., West A. — Banach and locally convex algebras

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Название: Banach and locally convex algebras

Авторы: Ya Helemskii A., West A.

Аннотация:

This text provides an up-to-date account of Banach and locally convex algebras with a particular emphasis on general theory, representations, and homology. In his descriptions and examples of general theory, the author remains aware of traditional trends in the field analysis while breaking from convention in his approach to "the algebra of analysis" through homological algebra. Such an approach allows Helemskii to consider topics not covered at this level in any other book, including complemented and uncomplemented ideals, projective and weak tensor products of banach algebras, Taylor's multivariable holomorphic functional calculus, the Wedderburn decomposition of Banach algebras, and the homology of Banach algebras. Graduate students and researchers in Banach algebras are sure to find this an invaluable volume.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 464

Добавлена в каталог: 12.05.2011

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Предметный указатель

Kadison's theorem      300
Kaplansky density theorem      157
Koszul complex      120
Koszul resolution      390
Krein — Milman theorem      13
Krull's lemma      84
Lassner algebra      158
Left action      278
Left approximate identity      75
Left Banach module      283
Left ideal      81
Left identity      60
Left invariant functional      352
Left invariant measure      167
Left inverse element      62
Left inverse morphism      20
Left module      278
Left outer multiplication      278
Left polynormed module      283
Length of a resolution      386
Lifting a morphism      338
Lifting problem      338
Liminal algebra      298
Linear complement      3
Linear isomorphism      3
Linearly interior point      11
Local observable algebra      150
Locally compact space      4
Locally convex = polynormed      6
Logarithm of an element      116
Long exact (co)homology sequence      54
Mashke's theorem      163
Maximal compactification      195
Maximal ideal      84
Measure algebra      174
Metric approximate identity      75
Minimal ideal      84
Modular ideal      86
Modular identity      86
Module      278 323
Module associated with a representation      278
Module morphism      279
Monomorphism      20
Monomorphism between the complexes      45
Morphism functor      22 328
Multi-C*-algebra      274
Multinormed seminorm      65
Multiple of a Hilbert space      143
Multiple of a system of seminorms      152
Multiplication      56
Multiplicatively polynormed algebra      65
n-dimensional coboundary      399
N-dimensional cochain      399
N-dimensional cocycle      399
n-dimensional cohomology      52
N-dimensional cohomology functor      52
n-dimensional homology      52
N-dimensional homology functor      52
n-irreducible module      308
n-irreducible representation      309
n-module      325
Naimark's theorem      315
Natural embedding      2
Natural equivalence      23
Natural module over operator algebra      290
Natural projection      3
Natural transformation between functors      22
Nest algebra      151
Nested system      151
Neumann series      77
Nilpotent element      92
Non-degenerate algebra      285
Non-degenerate module      284
Non-degenerate representation      284
Normal element      201
Normal operator      15
Normalized functional      352
Normed algebra      64
Nuclear C*-algebra      248
Nuclear operator      13
Nuclear space      43
Object over inverse system      257
Obstruction to lifting      397
One-dimensional coboundary      374
One-dimensional cocycle      373
One-dimensional cohomology group (of an algebra)      374
One-point compactification      5
Open map      4
Operator (semi)norm      9
Operator functor      22 328
Operator induced (by another operator)      3
Operator of tensor twisting      39
Opposite algebra      58
Order relation in a C*-algebra      250
Paracompact topological space      345
Phillips's theorem      17
Point inside a closed path      113
Point of an ideal      126
Point outside a closed path      113
Pointed category      24
Polydisc algebra      136
Polynomial of an element of an algebra      60
Polynormed function algebra      124
Polynormed module      283
Polynormed space      5
Pontryagin's duality principle      170
Positive element      201
Positive functional      208
Postliminal algebra      298
Pre-additive category      24
Pre-Hilbert space      6
Primitive algebra      303
Primitive ideal      301
Principal ideal      82
Problem of spectral synthesis      126
Problem of weak spectral synthesis      126
Product of elements of an algebra      57
Projective module      339
Projective on the left algebra      343
Projective resolution      386
Projective tensor product of Banach algebras      73
Projective tensor product of Banach spaces      32
Projective tensor product of polynormed spaces      40
Projective tensor product of seminorms      31
Proper ideal      82
Pure functional      319
Pure state      319
Quasicompact space      4
Quasilocal observable algebra      150
Quasinull element      91
Quotient *-algebra      202
Quotient algebra      87
Quotient module      279
Quotient norm      7
Quotient seminorm      7
Radical      92
Radical algebra      95
Radical extension      376
Rational function of an element of an algebra      63
Realized C*-algebra      138
Reduced C*-algebra      172
Reduced module      333
Regular measure      166
Regular point of an element      99
Regular representation      59
Replacement functor      327
Replicating homomorphism      143

Representation of an algebra      59
Resolution      386
Resolution of the identity      238
Resolvent      99
Retraction      20
Retraction problem      338
Right action      323
Right approximate identity      75
Right ideal      81
Right identity      60
Right inverse element      62
Right inverse morphism      20
Right module      328
Right outer multiplication      323
Sakai's theorem      244
Saturated system of seminorms      6
Schatten — von Neumann theorem      36
Schur's lemma      307
Segal's theorem      319
Self-adjoint element      200
Self-adjoint operator algebra      138
Self-adjoint part      200
Seminormed algebra      64
Seminormed space      5
Semisimple algebra      94
Separately continuous bi-operator      26
Sequence algebra      132
Shilov — Arens — Calderon — Waelbroeck theorem      118
Shilov's theorem on idempotents      192
Shirali — Ford theorem      221
Short complex      44
Short sequence      44
Simple algebra      97
Singular extension of an algebra      376
Singular point of an element      99
Skeleton of the projective ideal      346
Skew field      63
Space with strongest seminorm system      8
Spectral mapping theorem      117 121
Spectral measure      236
Spectral radius      105
Spectral synthesis      127
Spectrum functor      185
Spectrum of an element      99
Spectrum of commutative Banach algebra      183
Spectrum of commutative multinormed algebra      269
Split complex      46
Split extension      376 383
Splitting operator      377 383
Stable algebra      380
Stable module      380
Stable property      381
Standard bimodule resolution      389
Standard cohomology complex      399
Standard resolution      388
Star Banach algebra      202
Star boundary      210
Star functor      22 329
Star module      284
Star polynormed algebra      202
Star radical      215
Star semisimple algebra      232
Star-bounded algebra      210
Star-bounded element      210
State      207
Stone — Weierstrass theorem      223
Strong operator system of seminorms      28 152
Strong operator topology      28 152
Structure set      303
Structure space      305
Subalgebra      58
Subbase      4
Subcategory      20
Subdirect sum of algebras      304
Submodule      278
Taylor's theorem on a multi-operator holomorphic calculus      120
Tensor product of algebras      73
Tensor product of Banach algebras      73
Tensor product of Banach modules      330
Tensor product of Banach spaces      32
Tensor product of C*-algebras (maximal)      247
Tensor product of functionals      30
Tensor product of linear spaces (algebraic)      29
Tensor product of morphisms      334
Tensor product of operators      37
Tensoring functor      38
Theorem on the sufficiency of the set of characters      169
Three-dimensional coboundary      381
Three-dimensional cocyle      380
Three-dimensional cohomology group of an algebra      381
Tietze — Urysohn theorem      4
Topological complement      16
Topological isomorphism      10 286
Topological representation of an algebra      283
Topological square of a subset      66
Topologically cyclic module      300
Topologically cyclic representation      300
Topologically exact sequence      48
Topologically injective map      4
Topologically irreducible module      300
Topologically irreducible representation      300
Topologically nilpotent element      107
Topologically simple algebra      97
Translate of functions on a group      161
Two-dimensional coboundary      377
Two-dimensional cochain      377
Two-dimensional cocycle      377
Two-dimensional cohomology group (of an algebra)      378
Ultrastrong operator system of seminorms      152
Ultrastrong operator topology      28 152
Ultraweak operator system of seminorms      152
Ultraweak operator topology      152
Ultraweakly amenable von Neumann algebra      402
Uniform algebra      190
Uniqueness theorem for Fourier transforms      169
Uniqueness theorem for Fourier — Stieltjes transforms      199
Unital algebra      60
Unital homomorphism      60
Unital module      278 323
Unital norm      65
Unitarily equivalent operator      15
Unitary element      201
Unitary operator      15
Unitary representation of a group      291
Unitization of a homomorphism      61
Unitization of a module      278
Unitization of an algebra      61
Universal "-representation      214
Universality      28
Urysohn's theorem      4
Varopoulos space      36
Vector functional      207
Vector state      207
von Neumann algebra      157
von Neumann's bicommutant theorem      156
Weak operator system of seminorms      152
Weak operator topology      152
Weak system of seminorms      10
Weak tensor product of Banach spaces      39
Weak tensor product of polynormed spaces      41
Weak tensor product of seminorms      31
Weak topology      10
Wedderburn — Artin theorem      97
Wiener algebra      70
Yoneda product      49
Zero morphism      24
Zero object      24

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