Gohberg I., Goldberg S., Kaashoek M. — Classes of linear operators. (volume 2)
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Название: Classes of linear operators. (volume 2)
Авторы: Gohberg I., Goldberg S., Kaashoek M.
Аннотация:
This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering. Publication date: September 1993 Of interest to: Researchers, graduate students Codes: M16002, M16126, M16088, M16096 Classes of Linear Operators Vol. I This book presents a panorama of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. The present volume consists of four parts: general spectral theory, classes of compact operators, Fredholm and Wiener-Hopf operators, and classes of unbounded operators: The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering.
Dilation of an operator, isometric670 Dilation of an operator, minimal isometric670 Dilation of an operator, minimal unitary676 Dilation of an operator, N-step673 Dilation of an operator, one step673 Dilation of an operator, unitary676 Direct sum of Hilbert spaces657 Direct sum of operators on a Hilbert space658 Dirichlet operator316 Dirichlet operator, adjoint of321 Dissipative operator on a Banach space429 Dissipative operator on a Hilbert space428 Dissipative, i-dissipative506 Divergence form316 Divisor of zero796 Divisor of zero, topological796 Domain, Cauchy domain6 Domain, inner domain49 Domain, outer domain49 Douglas factorization lemma680 Eigenvalue of an unbounded operator349 Eigenvalue of finite type for a bounded operator25 Eigenvalue of finite type for an operator function205 Eigenvalue of finite type for an unbounded operator326 Eigenvector of an unbounded operator349 Eigenvector of an unbounded operator, generalized378 Elementary Blaschke factor748 Elementary pencil747 Elementary rotation748 Elementary solutions29 Embedding of an operator into a system716 Equivalence operator right54594 Equivalent, globally equivalent38 Equivalent, locally equivalent42 Equivalent, strictly equivalent237 Essential spectrum for a bounded operator191 Essential spectrum for an unbounded operator373 Excessive subspace707 Exponential representation268 Exponential type zero122 Extension -positive908 Extension band908943955 Extension central897899 Extension of a band matrix897 Extension of a lower triangular matrix902 Extension of an unbounded operator290 Extension one-step892 Extension positive897 Extension problem of Caratheodory — Toeplitz949 Extension problem of Nehari957 Extension strictly contractive902917 Extension triangular904917948961 Extension Z-extension38 Factorization canonical235588597832 Factorization indices235588832 Factorization, determined by746 Factorization, generalized LU550 Factorization, left spectral907 Factorization, left Wiener — Hopf235587 Factorization, LU545 Factorization, regular750 Factorization, right spectral842907 Factorization, right Wiener — Hopf235236587832 Factorization, spectral842 Factorization, supported by744 Factorization, Wiener — Hopf234585587832 Feedthrough operator704 Final space of a partial isometry84 Finite chain472 Finite slab problem274 Finitely meromorphic206 First kind Wiener — Hopf operator398 Fourier coefficients562 Fourier series563 Fourier transform217563792 Fourier transformation217563792 Fredholm operator, bounded184 Fredholm operator, perturbation of189376 Fredholm operator, unbounded372 Functional calculus1380323 Functional model733 Fundamental matrix154 Gelfand representation821 Gelfand spectrum820 Gelfand topology820 Gelfand transform820 Gelfand — Mazur theorem798 Gelfand — Naimark theorem846 Generalized Dirichlet problem316 Generalized eigenspace30 Generalized eigenvectors28378 Generalized inverse192 Generalized inverse in the weak sense193 Generalized LU-factorization550 Generalized resolvent equation50 Generalized Wiener — Hopf equations545 Generator of a semigroup419 Geometric multiplicity26 Globally equivalent38 Gramian controllability970 Gramian oberservability970 Graph norm369 Green’s formula304 Green’s function386 Half range problem258 Hankel operator225 Hankel operator, block574 Hardy space222562 Hilbert space chain476 Hilbert space direct sum of operators658 Hilbert space direct sum of spaces657 Hilbert — Schmidt norm143 Hilbert — Schmidt operator140 Hille — Yoshida — Phillips theorem418 Homomorphism821 Homomorphism, *-homorphism847 i-dissipative506 Ideal793 Ideal, maximal817 Ideal, proper793 Identity of a Banach algebra788 Index of a bounded Fredholm operator184 Index of a bounded semi-Fredholm operator283 Index of a unbounded Fredholm operator372 Indicator151 Infinitesimal generator of a semigroup419 Initial space of a partial isometry84 Inner domain49 Inner function660 input operator704776 Input space704 Integral operator148 Integral, along a chain485 Integral, multiplicative493 Interpolant, maximum entropy971 Interpolant, strictly contractive969 Interpolation problem, Carathedory — Schur692 Interpolation problem, Nevanlinna — Pick693962963 Interpolation problem, tangential Nevanlinna — Pick965 Invariant projectionally181 Invariant subspace8 Invariant subspace theorem478 Inverse794 Invertible794 Invertible, left807 Involution843 Isolated part of the spectrum9 Isometric dilation670 Isometric dilation, minimal670 Isometric semigroup431
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