Bognar J. — Indefinite Inner Product Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Bognar J. — Indefinite Inner Product Spaces

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Название: Indefinite Inner Product Spaces

Автор: Bognar J.

Аннотация:

By definition, an indefinite inner product space is a real or complex vector space together with symmetric (in the complex case: hermitian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values.
The main body of the text offers an introducion, with full proofs, to the subject. Prerequisites do not extend much beyond standart facts of linear algebra, topology, Hilbert and Banach space theory.
The notes at the end of each chapter contain, besides histirical and other comment relating to the main text, a survey of the literature on more avdanced topics such as the spectral function, groups and algebras of operators, application to differential equations and to quasi-definite functions, etc.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 224

Добавлена в каталог: 02.06.2005

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Предметный указатель

A-fundamental decomposition      36
A-inner product      36
A-isometric operator      36
A-isotropic part      36
A-orthogonal      36
A-orthogonal companion      36
A-orthogonal direct sum      36
A-orthogonal sum      36
A-positive subspace      36
A-positive vector      36
A-symmetric operator      30
Adjoint operator      121
Admissible topology      65
Algebraic multiplicity      29
Alternating extension      115
Alternating extension, maximal pair      115
Alternating extension, pair      114
Angular operator      54
Anti-space      6
Augmenting operator      162
Banach space with a J-metric      119
Banach space with a J-metric, topology      59
Basis      2
Cartesian product      8
Cayley transform      39
Cayley transform, transformation      39
Closed operator      121
Closed set      102
Closure of a set      102
Closure of an operator      121
Codimension      3 102
Commuting operators      30
Compact operator      120
Compact operator, set      120
Complementary subspace      2
Complete system      82
Completely invertible operator      29
continuous      102
Continuous spectrum      121
Convergent      102
Critical point      179
Decomposable space      24
Decomposition majorant      88
Definite inner product      5
Definite inner product, inner product space      5
Definite inner product, subspace      6
Degenerate inner product      9
Degenerate inner product, inner product space      9
Degenerate inner product, subspace      9
Dense      102
DIMENSION      2 102
Diminishing operator      162
Direct sum of operators      30
Direct sum of subspaces      2
Dissipative operator      116
Domain      2S
Doubly strict plus-operator      158
Dual companion for a subspace      21
Dual companion for a system      21
Dual pair of subspaces      21
Dual pair of systems      21
Eigenspace      29
Eigenvalue in a subspace      30
Eigenvalue of a quadratic pencil      172
Eigenvalue of an operator      29
Eigenvector      29
Elementary solution      172
Equivalent semi-norms      59
Frechet topology      59
Fundamental decomposition      24
Fundamental decomposition, projector      50
Fundamental decomposition, symmetry      52
Fundamentally reducible operator      163
Gram operator      89
Graph      121
Hilbert topology      59
Homeomorphic      102
Hypermaxjmal neutral subspace      15
Identity operator      28
Indefinite inner product      4
Indefinite inner product, inner product space      4
Indefinite inner product, subspace      5
Induced operator      30
Induced operator, topology      59
Inner product      3
Inner product, product space      3
Inner product, square      4
Intrinsic completion      71
Intrinsic completion, dimension      71
Intrinsic completion, norm      71
Intrinsic completion, topology      71
Intrinsically complete      71
Invariant subspace      29
Inverse operator      29
Invertible operator      29
Isometric operator      31
Isometrical isomorphism      4
Isometrically isomorphic      4
Isomorphic      1
Isomorphism      1
Isotropic part      9
Isotropic part, vector      9
J-adjoint      122
J-inner product      52
J-isometric operator      See A-isometric operator
J-norm      53
J-orthogonal      See A-orthogonal
J-orthogonal companion      See A-orthogonal companion
J-symmetric operator      See A-symmetric operator
Jordan chain of a quadratic pencil      172
Jordan chain of an operator      29
Krein space      100
Length of a Jordan chain      29
Linear form      2S
Linear operator      2S
Linearly independent subspaces      2
Linearly independent vectors      2
Locally convex topology      5S
Mackey topology      96
Majorant      77
Maximal definite subspace      12
Maximal dissipative operator      117

Maximal negative definite subspace      12
Maximal negative subspace      12
Maximal neutral subspace      12
Maximal non-degenerate subspace      12
Maximal positive definite subspace      12
Maximal positive subspace      12
Maximal rectangular isometric operator      128
Maximal semi-definite subspace      12
Maximal uniformly negative subspace      112
Maximal uniformly positive subspace      112 minimal majorant S4
Maximal unitary dilation      139
Natural norm      102
Negative definite inner product      5
Negative definite inner product space      5
Negative definite subspace      6
Negative inner product      5
Negative inner product space      5
Negative subspace      6
Negative vector      4
Neutral inner product      5
Neutral inner product space      5
Neutral part      4
Neutral set      4
Neutral subspace      6
Neutral vector      4
Non-strict plus-operator      46
Non-uniformly definite subspace      109
Normal eigenvalue      121
Normed topology      59
Null space (of an operator)      28
Operator matrix      30 ortho-complemcnted
Operator, companion      7
Operator, direct sum      7
Operator, projector      36
Operator, sum      7
Orthonormal system      81
Partial majorant      59
Pesonen operator      4S
Plus-defect of a subspace      107
Plus-defect of an operator      157
Plus-operator      45
Point spectrum of a quadratic pencil      172
Point spectrum spectrum of an operator      121
Polar of a norm      64
Polar of a topology      64
Polarization formula      4
Pontrjagin space      184
Positive definite inner product      5
Positive definite inner product space      5
Positive definite subspace      0
Positive inner product      5
Positive inner product space      5
Positive operator      147
Positive subspace      6
Positive vector      4
Positizable operator      180
Positizing polynomial      18O
Principal subspace      29
Principal vector      29
Projection      15
Quadratic pencil      172
Quadratic pencil semi-norm      58
Quadratic-normed topology      59
Quasi-A-positive inner product      36
Quasi-A-positive inner product space      36
Quasi-negative inner product      25
Quasi-negative inner product space      25
Quasi-positive inner product      25
Quasi-positive inner product space      25
Quotient, space      3 11
RANGE      28
Rank of A-negativity      149
Rank of A-positivity      149
Rank of an operator      2S
Rank of indefiniteness      95
Rank of negativity      51 95
Rank of positivity      51 95
Rectangular isometric operator      128
Reducing direct decomposition      30
Regular point of an operator      121
Regular subspace      71
Regular symmetric extension      197
Residual spectrum      121
Resolvent set of a quadratic pencil      1
Resolvent set of an operator      121
Restriction of an operator      30
Second orthogonal companion      7
Self adjoint operator      133
Self-polar topology      65
Semi-definite inner product      5
Semi-definite inner product space      5
Semi-definite subspace      6
Semi-norm      58
Semi-simple eigenvalue      29
Separable topology      89
Separated topology      59
Singular subspace      71
span      1
Spectral function      178 180
Spectrum of a quadratic pencil      174
Spectrum of an operator      121
Strict plus-operator      46
Strong topology      102
Stronger topology      59
Strongly damped      183
subspace      1
Symmetric operator      34
Topology defined by semi-norms      58
Uniformly definite subspace      108
Uniformly negative subspace      107
Uniformly positive operator      151
Uniformly positive subspace      107
Unimodular number      31
Unitary dilation      139
Unitary operator      128
Vector space      1
Vector sum      2
Weak operator topology      120
Weak topology      60
Weaker topology      59
Weakest majorant      87
Zero operator      28
Zero subspace      1

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