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Douglas R.G. — Banach algebra techniques in operator theory
Douglas R.G. — Banach algebra techniques in operator theory

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Название: Banach algebra techniques in operator theory

Автор: Douglas R.G.

Аннотация:

Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. At the end of each chapter there are source notes which suggest additional reading along with giving some comments on who proved what and when. In addition, following each chapter is a large number of problems of varying difficulty. This new edition will appeal to a new generation of students seeking an introduction to operator theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 216

Добавлена в каталог: 08.02.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
*-homomorphism      88 110
Absolute continuity, of measures      104
Absolutely convergent Fourier series      56 61
Abstract index      36 62 133 138
Abstract index group      36 38
Adjoint of bounded linear transformation      30
Adjoint of closed, densely defined linear transformation      119
Adjoint of Hilbert space operator      81—82
Alaoglu theorem      10
Algebra of bounded holomorphic functions      26 150
Annihilator, of subspace      30 80
Asymptotically multiplicative functions      169
Atkinson theorem      128
Automorphism of Banach algebra      61
Automorphism of C*-algebra, inner      143
Automorphism of C*-algebra, weak      144
Banach algebra      34 32—62
Banach space      2 1—31
Banach theorem      13 31
Beurling theorem      45 153
Bilateral shift      89
Boundary, for function algebra      61
Bounded below, operator      83
Bounded variation, function      14
Brown — Halmos theorem      182
C*-algebra      91
Calkin algebra      127
Cauchy — Schwarz inequality      64
Cech cohomology group      38
Center, of algebra      196
Characteristic function      18
Circle group      51
Classical index      130 138
Closed convex hull      182
Closed graph theorem      29
Cobum theorem      184 185 205
Cohomotopy group      39
Commutant, of algebra      108
Commutator      180
Commutator, ideal      145 179
Compact operator      121 145
Complete metric space      2
Conjugate space      6
Convolution product      54
Corona theorem      156 173
Cross-section map      178
Cyclic vector      105 157
Dimension, Hilbert space      76 79
Direct sum of Banach spaces      29
Direct sum of Hilbert spaces      78
Directed set      3
Dirichlet problem      171
Disk algebra      51—53
Division algebra      42
Eigenspace, generalized      131
Essential range      57
Essential resolvent      191
Essential spectrum      190 191
Essentially bounded      24
Exponential map      36
Extensions, of C*-algebras      205
Extreme point      28 78
Fatou theorem      174
Fiber, of $M_{\infty}$      172
Finite rank operator      59 121
Fourier coefficient      55
Fourier series      55
Fredholm alternative      131
Fredholm integral operator      125
Fredholm operator      127
Fuglede theorem      114 120
Function algebra      51
Functional calculus      93 99
Functional calculus, extended      112—114
Gelfand theorem      44 45
Gelfand transform      40
Gelfand — Mazur theorem      42
Gelfand — Naimark theorem      93
Gleason — Whitney theorem      164
Gohberg theorem      146
Gohberg — Krupnik theorem      207
Gram — Schmidt orthogonalization process      79
Grothendieck theorem      30
Hahn — Banach theorem      11 12 78
Hankel matrix      203
Hankel operator      203
Hardy space      26 70 149—176
Harmonic extension      168
Hartman theorem      183 204
Hartman — Wintner theorem      179 183
Hausdorff-Toeplitz theorem      115
Hellinger — Toeplitz theorem      116
Helson — Szego theorem      187
Hermitian operator      84
Hilbert space      63—80 66
Idempotent operator      116—117
Indicator function      see Characteristic function
Initial space, of partial isometry      95
Inner function      152
Inner product      63
Inner product space      64
Inner-outer factorization      158
Integral operator      125 132 145
Invariant subspace      98
Invariant subspace, simply      151—152
Involution, of Banach algebras      82 91
Irreducible subset      141
Isometry      95 117 146
Isomorphism, of Hilbert spaces      76
Jensen's inequality      174
Kernel of integral operator      126
Kernel of operator      83
Kolmogrov — Krein theorem      175
Krein theorem      147
Krein — Mil'man theorem      28
Krein — Smul'yan theorem      30
Lebesgue space      7 23—26 68—70
Linear functional      5 72
Linear transformation, bounded      21
Linear transformation, closable      118
Linear transformation, closure of      118
Linear transformation, self-adjoint      119
Linear transformation, symmetric      119
Localization, of C*-algebras      196
Matrix operator entries      116--117
Maximal abelian subalgebra      88
Maximal ideal space      44
Metric      2
Metric space      2
Multiplication operator      87
Multiplicative linear functional      32 39
Nehari theorem      203
Net      3
Net, Cauchy      3
Newman theorem      173
Norm      1
Norm, Hilbert space      64
Normal element, in C*-algebra      91
Normal operator      84
Normed linear space      4 27
Numerical radius      115
Numerical range      115
Open mapping theorem      22 23
Operator      81
Orthogonal      65
Orthogonal complement      71
Orthonormal      65 79
Orthonormal basis      74—75
Outer function in $H^1$      172 174
Outer function in $H^2$      157
Parallelograrn law      66
Partial isometry      95
Piecewlse continuous function      176
Polar decomposition      97 98
Polar form      95
Polarization identity      64
Polynomials, analytic trigonometric      51
Polynomials, trigonometric      51
Positive element, of C*-algebra      94 117
Positive operator      84
Projection      86
Pure isometry      173
Pure isometry, multiplicity      173
Putnam theorem      120
Pythagorean Theorem      66 73
Quasicontinuous function      176
Quasinilpotent operator      133 145
Quotient algebra      43
Quotient C*-algebra      139
Quotient space      20
Radical ideal, of Banach algebra      60
Radon — Nikodym theorem      25 80
Range, of operator      83
Reducing subspace      98
Reflexive Banach spaces      28—30
Resolvent set      41
Riemann — Stieltjes integral      15
Riesz (F. and M.) theorem      154
Riesz functional calculus      60
Riesz representation theorem      72
Riesz theorem      18
Riesz — Markov representation theorem      20
Self-adjoint element, of C*-algebra      91
Self-adjoint operator      84
Self-adjoint subset      46
Semisimple algebra      60
Separating vector      105
Silov boundary      61 164 173
Silov theorem      53
Similarity, of operators      117
Spectral inclusion theorem      179 188
Spectral mapping theorem      45
Spectral measure, scalar      113
Spectral projection      113
Spectral radius      41
Spectral subspace      113
Spectral theorem      93
Spectrum      41
Spectrum operator      85
Square root, of operator      95
State      147
State, pure      147
Stone — Cech compactification      58 59
Stone — Weierstrass theorem      46
Stone — Weierstrass theorem, generalized      50
Strong operator topology      100
Subharmonic function      174
Sublinear functional      11
Subnormal operator      183
Summability, in Banach space      4
Symbol, of Toeplitz operator      184
Symmetric linear transformation      see Linear transformation symmetric
Szego theorem      175
Szego — Nagy theorem      173
Tensor product of Banach algebras      62
Tensor product of Banach spaces      31
Tensor product of Hilbert spaces      79
Tensor product of operators on Hilbert spaces      118
Toeplitz matrix      177
Toeplitz operator      177
Uniform boundedness theorem      29
Unilateral shift      96 117 136
Unit ball, of Banach space      10
Unitary element, of C*-algebra      91
Unitary equivalence, of operators      117
Unitary operator      84 117
Volterra integral operator      132
von Neumann double commutant theorem      118
von Neumann theorem      173
von Neumann — Wold decomposition      173
W*-algebra      101
w*-topology      9 30 78
w-topology      29
Weak operator topology      100
Weak topology      9
Weierstrass theorem      48
Weyl theorem      145
Weyl — von Neumann theorem      146
Widom theorem      195 207
Widom — Devinatz theorem      204
Wiener theorem      56
Wiener — Hopf operator      200
Wintner theorem      183
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