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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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1993Количество страниц: 564Добавлена в каталог: 16.06.2005Операции: Положить на полку |
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Isometry 654 Isometry, pure 654 Isomorphism 821 Isomorphism, *-isomorphism 847 Jordan chain 28 Jump of a chain 474 Jump, dimension of 474 Kernel function 148 215 Kernel function, order of 539 Kernel function, semi-separable 149 538 Lagrange adjoint for an ordinary differential expression 301 309 Lagrange adjoint for the Dirichlet problem 318 Laplace transformation 418 Laurent operator, block 564 Lax — Milgram lemma 319 Left invertible 807 Left strictly equivalent 237 Left Wiener — Hopf factorization 235 587 Lemma of Schur 31 Lifting of an operator 689 Linear functional, multiplicative 811 Linear functional, positive 852 Linear operator pencil 49 Linearization 38 642 Locally equivalent 42 Lower order 149 LU-decomposition, additive 473 488 LU-decomposition, multiplicative 513 LU-factorization 513 545 LU-factorization, generalized 550 Lyapunov’s theorem 22 Main operator 704 776 Matricially coupled 44 Matricially coupled, analytically 46 Matrix Wiener algebra 806 Matrix Wiener algebra on the line 834 Maximal ideal 817 Maximal operator 295 Maximal operator, adjoint of 301 Maximum entropy, interpolant 971 Maximum entropy, principle 901 904 931 Min-max theorem 96 Minimal closed linear extension 289 Minimal operator 300 Minimal operator, adjoint of 301 Minimal realization 736 Minus function 583 Multiplication, operator of 218 Multiplicative diagonal, left 933 Multiplicative diagonal, right 932 943 Multiplicative integral 493 Multiplicative integral, convergence of 493 Multiplicative linear functional 811 Multiplicity, algebraic multiplicity 26 205 Multiplicity, geometric multiplicity 26 Multiplying medium 275 Mutually disjoint projections 88 Nehari extension problem 957 Nevanlinna — Pick interpolation problem 693 962 Nevanlinna — Pick interpolation problem, matrix version 963 Nevanlinna — Pick interpolation problem, tangential 965 Nilpotent element 802 Non-negative element in a C*-algebra 849 933 Non-negative operator 82 Normal element in a C*-algebra 848 Normal with respect to a contour 205 Numerical range 167 Observability Gramian 970 Observable, approximately 710 One-step extension, center of 896 One-step extension, central 897 One-step extension, radius of 896 Open neighbourhood of a set 13 Operator band 939 operator function 695 Operator lower triangular part 946 Operator with compact resolvent 328 Operator, bounded selfadjoint 61 Operator, closable 289 Operator, completely non-unitary 700 Operator, compression of 666 Operator, contraction 665 Operator, convolution 216 Operator, differential 295 382 399 Operator, dilation of 667 Operator, Dirichlet 316 Operator, dissipative 428 429 Operator, Fredholm 184 372 Operator, Hankel 574 Operator, Hilbert — Schmidt 140 Operator, Laurent 564 Operator, non-negative 82 Operator, of multiplication 218 Operator, rotation 666 Operator, semi-Fredholm 283 Operator, strictly negative 22 Operator, strictly positive 22 Operator, Toeplitz 561 570 Operator, trace class 105 Operator, unbounded selfadjoint 341 Operator, unicellular 511 Operator, unitary 85 Operator, Volterra 32 Operator, Wiener — Hopf 221 Order of a semiseparable representation 149 539 Order of a semiseparable representation, lower 149 Order of a semiseparable representation, upper 149 Order of a Sobolev space 313 Order of the differential expression 310 Outer domain 49 output operator 704 776 Output space 704 Part of an operator 658 Partial integration, formula of 488 Partial isometry 84 Partial isometry, final space of 84 Partial isometry, initial space of 84 Partition of a chain 474 Partition of a chain, finer 474 PC topology 879 Permanence principle 901 Plus function 583 Polar decomposition 84 Positive completion of an operator band 939 Positive definite element in a *-algebra 907 Positive definite element in a C*-algebra 857 Positive definite matrix 897 Positive extension 897 908 Positive extension, 908 Positive linear functional 852 Positive semidefinite 933 Principal part of a unitary system 709 Principal subspace 707 Problem of completeness 29 Product of systems 737 777 Projection of a symmetric system, left 778 Projection of a symmetric system, right 778 Projection of a unitary system, left 743 Projection of a unitary system, right 744 Projectionally invariant 181 Pure isometry 654 Pure unitary system 709 Quasi-nilpotent 802 Quotient algebra 793 Radical 828 Realization 244 593 723 Realization in the class of 723 Realization, canonical 732 Realization, minimal 736 Realization, restricted shift 736 Realization, stable 969 Realization, unitary 723 Realized form 244 395 593 Reducing subspace 866 Reduction relative to a chain 474 Regular 49 Regular factorization 750 Regular, 49 Representation Gelfand 821 Representation of a C*-algebra 853 Reproducing kernel 496 Reproducing kernel, Hilbert space 496 Resolution of the identity 72 350 362 Resolution of the identity for a bounded selfadjoint operator 74 Resolution of the identity for an unbounded selfadjoint operator 362 Resolution of the identity, bounded 72 Resolvent equation 9 288 Resolvent equation, generalized 50 Resolvent identity 288 Resolvent operator 6 288 Resolvent set 5 49 288 Resolvent set of a Banach algebra element 797 Restricted shift realization 736 Restriction of an unbounded operator 290 Restriction to an invariant subspace 8 Riesz projection 9 326 Right canonical factorization 235 588 Right equivalence operator 54 594 Right factorization indices 235 588 Right Wiener — Hopf factorization, relative to the circle 236 587 Right Wiener — Hopf factorization, relative to the real line 235 RKHS 496 Rotation operator 666 Rotation, elementary 748 Row multiplicity 238 S-number 96 212 Scattering function 258 Schmidt-representation 97 Schur basis 136 Schur’s lemma 31 Selfadjoint element in a *-algebra 907 Selfadjoint element in a C*-algebra 844 Selfadjoint operator 61 341 Semi-Fredholm operator 283 Semi-invariant subspace 668 Semi-separable kernel function 149 538 Semi-separable kernel function, order of 539 Semi-separable representation 149 Semi-separable representation, lower order of 149 Semi-separable representation, order of 149 539 Semi-separable representation, upper order of 149 Semi-simple Banach algebra 828 Semigroup, 415 Semigroup, compact 435 Semigroup, completely non-unitary 703 Semigroup, contraction 427 Semigroup, isometric 432 Semigroup, strongly continuous 415 Semigroup, translation 420 Semigroup, unitary 432 Separate points of 845 Separating projection 54 Sesquilinear form 319 Sesquilinear functional 858 Shift, backward 656 Shift, block forward 656 Shift, forward 655 Simple pole 88 Singular value 96 212 Singular value decomposition 98 Sobolev space 313 Solution of a half range problem 441 Solution of an abstract Cauchy problem 408 Solution of an abstract Cauchy problem, 408 Solution of an abstract Cauchy problem, continuously differentiable 408 Solution, elementary solution 29 Spectral decomposition 54 Spectral factorization 842 Spectral factorization in an algebra with band structure 907 Spectral factorization in an left 907 Spectral factorization in an right 907 Spectral mapping theorem 16 Spectral mapping theorem in a C*-algebra 849 Spectral measure 362 859 Spectral measure, associated with T 864 Spectral radius 90 Spectral radius of a Banach algebra element 800 Spectral subspace 59 Spectral subspace, corresponding to the left (right) half plane 336 Spectral theorem for a normal operator 863 Spectral theorem for a selfadjoint operator, bounded 77 Spectral theorem for a selfadjoint operator, unbounded 350 Spectrum of a Banach algebra element 797 Spectrum of a bounded operator 5 Spectrum of an operator pencil 49 Spectrum of an unbounded operator 288 Spectrum, Gelfand 820 Square root of an operator 83 Stable realization 969 Standard unitary system 743 State space 704 776 State space operator 704 776 Stone — Weierstrass theorem 845 Strict contraction 702 Strictly 935 Strictly contractive, completion 917 946 Strictly contractive, extension 902 917 Strictly contractive, interpolant 969 Strictly negative operator 22 Strictly positive element of a C*-algebra 856 Strictly positive operator 22 Strictly proper function 969 Strong operator topology 476 Strongly continuous semigroup 415 Strongly decomposable algebra 545 Subalgebra of 845 Subalgebra of a Banach algebra 788 Subalgebra, *-subalgebra 847 Subalgebra, generated by 825 subspace 5 Support of a function 300 310 Supporting subspace 746 Symbol 640 877 883 Symbol of a (block) Toeplitz operator 623 630 635 879 Symbol of a convolution operator 216 Symbol of a differential operator 399 Symbol of a Wiener — Hopf operator 221 Symmetric operator 347 Symmetric system 776 System matrix 705 System, cascade connection of 737 777 System, controllable 711 System, finite dimensional 704 System, principal part of 709 System, product of 737 777 System, pure 709 System, standard unitary 743 System, symmetric 776 System, transfer function of 705 776 System, unitary 705 Szegoe limit formula, first 617 Szegoe limit formula, second 617 T-bounded 369 T-compact 370 T-norm 369 Toeplitz operator 570 Topological divisor of zero 796 Topology Gelfand 820 Topology PC 879 Totally bounded 314
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