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Авторизация |
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Поиск по указателям |
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Arveson W. — A Short Course on Spectral Theory |
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Предметный указатель |
11M
110
108
108
12
8
93
110
6
-representation 60
64
96
Absolutely convergent seria 8 11
Adjoint of an operator 40
Algebra, Banach 8
Algebra, complex 7
Algebra, disk 8
Algebra, division 17
Algebra, group 10
Algebra, matrix 8
Algebra, normed 8
Asymptotic invariant 83 85
Atkinson’s theorem 93
Banach -algebra 57
Banach algebra 8
Banach limit 85
Basis for a vector space 24
Beurling’s theorem 118
Beurling’s theorem, proof of 120
C(X) 8
C-algebra of operators 42
Calkin algebra 83
Carona of 81
Closed convex bull 28
Coburn’s theorem 119
Cokernel 87
Commutant of a set of operators 43
Commutative C-algebras, characterization of 47
Compact operator 13 68
Convex bull 28
Coordinate systems and unitary operators 52
Current variable 31 64 69 105 100 112
Curve 34
CYCLE 35
Cyclic representation 59
Diagonalizable operator 53
Direct sum of representations 57
Disk algebra 8
Division algebra 17
Equivalent representations 58
Essential range of 44
Essential representation 57
Essential spectrum 94
Exact sequence 21
Exponential map 47
Extension, split 112
Extension, Toeplita 112
F. and M. Riesz theorem 118
Finite-rank operator 13
Fredbolm index 95
Fredholm alternative 87
Fredholm operator on a Banach space 93
Free Abelian group 35
Functional calculus, analytic 33 37
Functional calculus, Borel 63
Functional calculus, continuous 51
Gelfand spectrum 28
Gelfand spectrum, compactness of 25
Gelfand — Mazur theorem 19
Gelfand — Naimark theorem 129
Gelland map 26
General linear group 14
General linear group, openness 14
GNS construction 122
GNS pair for states on Banach -algebras 123
GNS pair, exlatance 133
GNS pair, inequality 123
Group algebra 10
Haar measure 10
Hartman theorems 122
Hausdorff maximality principle 23
Hilbert — Schmidt operator 70
Hold of 32
Ideal 21
Ideal in C-algebra 70
Ideal, numerical 23
Ideal, proper 21
Index of a linear transformation 80
Index of a product 97
Index of Toeplitz operators 116
Index, continuity of 99
Index, of a bounded operator 95
Index, stability of 68
Integral equations, Volterra 4
Interior of a cycle 36
Invertible element of a Banach algebra 14
Invertible operator 6
Involution 41
Isometry 41
Isomorphism of Banach algebras 17
K(E) 80
Kernel 87
Linearly ordered set 23
Linearly ordered subset, maximal 29
lnductive partially ordered set 23
Locally analytic function 30
MASA 102
Maximal abelian von Neumann algebra 102
Maximal element 23
Maximal ideal 23
| Maximal ideal space 26
Maximal ideal, closure or 23
Multiplication algebra 44
Multiplication operator 43
Multiplicity-free operator 103
Neumann series 7 14
Nondegenerate representation 67
Normal operator 41
Numerical radius 45
Numerical range 45
Oriented curve 34
Partially ordered set 23
Polarization formula for linear forms 45
Polarization formula for operators 72 75
Positive linear functional 123
Positive operator 41
Projection 41
Proper ideal 21
Pure isometry 113
Pure state 120
Quasinilpotent operator 20
Quotient, algebra 21
Quotient, Banach algebra 22
Quotient, C-algebra 79
Quotient, norm 22
R(X) 19
Radical 27
Radon measure 10
Range of a *-homomorphism 80
Rank of an operator 13
Reducing subspace 113
Regular representation 13
Representation, cyclle 50
Representation, direct sum 57
Representation, essential space of 67
Representation, nondegenerale 67
Representation, norm of 68
Representation, of a Banach *-algebra 87
Representation, subrepresentation of 58
Resolution of the identity 67
Resolvent, estimates 14
Resolvent, set 6
Riesz lemma for operators 40
Riesz lemma for vectors 30
Runge’s theorem 33
Schwarz inequality for positive linear functionals 123
SCROC 34
Semisimple 27
Separable C*-algebra 105 129
Separable measure space 43
Set, inductive 23
Set, linearly ordered 23
Set, partially ordered 23
Shift, bilateral 104
Shift, unilateral 110
Shift, weighted 18
Simple algebra 21
Simple topologically 22 24
sp(A) 25
Spectral mapping theorem 19
Spectral measure 66
Spectral permanence for Banach algebras 32
Spectral permanence, C*-algebras 49
Spectral radius 19
Spectral radius formula 19
Spectral theorem 65
Spectrum and Gelland theorem 36
Spectrum and solving equations 2
Spectrum and the complex number field 2
Spectrum in a Banach algebra 10
Spectrum of a compact operator 87
Spectrum of a multiplication operetor 44
Spectrum of a Toeplitz operator 121 123
Spectrum of an operator 6
Spectrum, compactness 10
Spectrum, Gelfend 25
Spectrum, nontriviality 16
State 122
State, pure 129
Stone — Cech compactification of X 81
Subrepresentation 58
Symbol of a Toeplitz matrix 109
Symbol of Toeplitz operator 107
Tauberian theorems 29
Toeplitz C*-algebra 110
Toeplitz matrix 101 107
Toeplitz operator 101 107
Toeplitz operator, characterization of 107
Toeplitz operator, index of 110
Toeplitz operator, spectrum of 121 122
Topology, locally convex 42
Topology, strong operator topology 42
Topology, weak operator topology 42
Trace class operator 71
Unilateral shift 110
Unit of an algebra 7
Unit, approximate 9
Unital algebra 7
Unitarily equivalent representations 58
Unitary operator 41
von Neumann algebra 42 102
Weighted shift 18
Weyl spectrum 93
Widow’s theorem 121
Wiener algebra 29
Winding number of a curve 35
Winding number of a cycle 36
Winding number of an element or 115
Wold decomposition 113
Zorn’s Lemma 23
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