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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l^{1}$-algebra (complete) of a group      159
$m\underline{s}$-topology      152
$m\underline{w}$-topology      152
$\mathcal{H}^{1}(A,X)$      374
$\mathcal{H}^{2}(A,X)$      378
$\mathcal{H}^{3}(A,X)$      381
$\mathcal{H}^{n}(A,X)$      399
$\underline{m}$-topology      232
$\underline{s}$-topology      152
$\underline{w}$-topology      152
*-algebra      139 200
*-automorphism of *-algebras      139
*-character of a *-algebra      201
*-homomorphism of *-algebra      139
*-ideal      201
*-isomorphism of algebras      200
*-map      200
*-operator      200
*-representation of a *-algebra      139 205
*-subalgebra      202
*-subset      201
A-B-bimodule      323
A-bimodule      323
Absolutely continuous character      176
Absorbing set      11
Additive category      25
Adjoint element      200
Admissible complex      382
Admissible epimorphism      339
Admissible extension problem      348
Admissible lifting problem      339
Admissible monomorphism      348
Admissible morphism      382
Alexandrov's Theorem      4
Algebra      56
Algebra automorphism      66 369
Algebra of slowly increasing sequences      133
Algebra with a continuous inverse      102
Algebra, Arens — Michael      65
Algebra, Calkin      145
Algebra, Fermion      147
Algebra, Fourier      160
Algebra, Frechet      64
Algebra, isomorphism      18
Algebra, Lassner      158
Algebra, local observable      150
Algebra, quasi-local observable      150
Algebra, von Neumann      157
Algebraic square of a subset      58
Amenable algebra      356
Amenable group      352
Annihilator      280
Annihilator module      280
Approximate diagonal      360
Approximate identity      360
Arens — Michael algebra      65
Arens — Michael hull of a polynormed algebra      264
Arithmetic root of an element      231
Associativity of the product      57
Associativity of the tensor product      39
Augmentation ideal      162 291
Augmentation module      291
Augmentation morphism      291
Balanced bi-operator      330
Banach algebra      64
Banach complement      16
Banach function algebra      124
Banach module      283
Banach operator algebra      138
Banach space      16
Banach theorem      13
Banach — Alaogli theorem      11
Banach — Steinhaus theorem      12
Base space      288
Basic lemma of homological algebra      52
Basis of module      281
Bi-ideal      81
Bi-operator      3
Bi-operator (semi)norm      26
Bicommutant      155
Biflat algebra      356
Bifunctional      3
Biprojective algebra      356
Borel function      232
Borel function of an operator      233
Borel functional calculus      233
Borel set      232
Bounded approximate identity      75
Bounded bi-operator      26
Bounded representation of a group      291
C*-algebra      223
C*-algebra (complete) of a group      246
C*-approximation      36
C*-norm      223
C*-property      14 224
C*-seminorm      224
Calkin algebra      145
Calkin theorem      142
Canonical embedding      349
Canonical morphism      342
Canonical projection      340
Cartesian product of algebras      72
Category isomorphism      23
Category of Banach algebras      66
Category of Banach modules      286 324
Category of polynormed algebras      66
Category of polynormed modules      286 324
Centre of a bimodule      374
Centre of an algebra      58
Chain complex      44
Character of a group      164
Character of an algebra      59
Classical semisimple algebra      95
Closed graph theorem      13
Co-free functor      330
Co-free module      348
Cochain complex      44
Codomain      1
Cohomology group (of an algebra)      399
Cohomology of a complex      52
Commutant      155
Commutative algebra      57
Commutative diagram      2 19
Commutative elements      57
Commutativity of tensor product      38
Compact space      4
Compact-open system of seminorms      8
Compact-open topology      8
Compactification      194
Comparison theorem      386
Compatible family of inverse systems      259
Complemented submodule of a module      286
Complemented subspace      16
Complete direct sum of an algebra      304
Complete Hausdorff inductive tensor product      40
Complete Hausdorff projective tensor product      40
Complete polynormed space      7
Complete subcategory      20
Completion      68
COMPLEX      44
Complex manifold over $\mathbb{C}^{n}$      134
Complex over a module      386
Component short exact sequence      49
Concomitant Banach algebra      256
Concomitant homomorphism      257
Conditional unitization      62
Connecting operator      54
Continuous function of an element of an algebra      231
Continuous functional calculus      228
Continuous homomorphism      65
Continuous morphism      285
Contractible algebra      356
Contractible homotopy      46
Convolution of functionals      174
Convolution of functions      159 167
Convolution of generalized functions      177
Convolution of measures      174
Corestriction of map      2
Coretraction      20
Coretraction problem      352
Corona problem      138
Criterion for operators to be positive      15
Cyclic element      294
Cyclic module      294
Cyclic representation      294
Decomposition of a right approximate identity      343
Defining system of seminorms      6
Derivation of an algebra      369
Derived functor      391
Diagonal of the algebra      360
Diagram      2
Differential of a complex      44
Direct sum diagram      24
Direct summand      24
Disc algebra      136
Discrete character      176
Domain      1
Dual (bi)module      324
Dual associativity      38 335
Dual complex      45
Dual module      324
Dual space      10
Elementary tensor      30 331
Envelope of holomorphy      135
Enveloping Banach algebra of a Banach algebra      236
Enveloping C*-algebra of a $\times$-algebra      245
Epimorphism      20
Equivalent extensions of algebras      376
Equivalent extensions of modules      383
Equivalent representations      279
Essential part of a module      284
Essential submodule      284
Exact complex      47
Exact sequence      47
Exact sequence of complexes      53
Exponential of an element      111
Extension of a module      383
Extension of a morphism      348
Extension of an algebra      375
Extension problem      352
Faithful module      280
Fermion algebra      147
Field      63
Final object      24
Finitely generated algebra      58
Finitely generated module      280
Fixed character      139
Fixed ideal      126
Flat module      351
Forgetful functor      327
Fourier algebra      160
Fourier transform      169
Fourier transformation of a $L^{1}$-algebra      169
Fourier — Stieltjes transform      199
Frechet algebra      64
Frechet space      7
Free banach module      288
Free module (simple)      281
Free unital Banach module      287
Free unital module (pure)      281
Freedom functor      387
Freezing isomorphism      27
functor      21
Functor of tensoring by a module      334
Gel'fand topology      183
Gel'fand transform of an element of a commutative Banach algebra      187
Gel'fand transform of the element of a locally multiplicatively convex algebra      270
Gel'fand transformation of a commutative Banach algebra      189
Gel'fand transformation of a locally multiplicatively convex algebra      270
Gel'fand — Kolmogorov theorem      127
Gel'fand — Mazur theorem      103
Gel'fand — Naimark theorem (the first)      226
Gel'fand — Naimark theorem (the second)      243
Gel'fand's theorem on holomorphic calculus      114
Gel'fand's theorem on realization by holomorphic functions      190
Generators of a module      280
Generators of an algebra      58
Gleeson topology      187
Global homology dimension      406
GNS-construction      208
GNS-representation      210
Group algebra      58 158
Haar measure      167
Hahn — Banach theorem      11
Hereditarily paracompact space      345
Hereditary on the left algebra      343
Hermitian algebra      218
Hilbert algebra of a group      173
Hilbert space      7
Hilbert space associated with positive functional      209
Hilbert sum of Hilbert spaces      214
Hilbert sum of representations      214
Hilbert — Schmidt *-operator      141
Holomorphic function of the element of an algebra      109
Holomorphic function on a complex manifold      134
Holomorphic vector function      42
Homological dimension of a module      403
Homology of a complex      52
Homomorphism of algebras      58
Homomorphism theorem      90
Homotopy      45
Homotopy equivalence      45
Hull of the subset of an algebra      186 305
Hull-kernel topology      186 305
Ideal      81
Idempotent element      92
Identity of an algebra      60
Inductive tensor product      40
Initial object      24
Injective coresolution      389
Inner automorphism      373
Inner derivation      373
Integral of a vector function along the path      112
Integral with respect to the spectral measure      237
Intertwining      279
Invariant subspace problem      316
Inverse element      62
Inverse limit      261
Inverse morphism      20
Inverse system in categories      257
Invertible element      62
Invertible on the left element      62
Invertible on the right element      62
Involution      200
Irreducible module      295
Irreducible operator algebra      295
Irreducible representation      295
Isometric homomorphism      66
Isometric isomorphism      66
Isometric operator      10
Isomorphic categories      23
Isomorphic modules      279
Isomorphisms of the objects of categories      20
Jacobson — Chevalley Density Theorem      309
Johnson's theorem on automatic amenability      365
Johnson's theorem on automatic continuity      313
Joint Shilov spectrum      118
Joint taylor spectrum      120
Jointly continuous bi-operator      26
Jointly polynormed algebra      71
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