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A -fundamental decomposition 36 convergent 102 A-inner product 36 critical point 179 A-isometric operator 36 A-isotropic part 36 decomposable space 24 A-orthogonal 36 decomposition majorant 88 companion 36 definite inner product 5 - direct sum 36 - inner product space 5 - sum 36 - subspace 6 A-positive subspace 36 degenerate inner product 9 - vector 36 - inner product space 9 A-symmetric operator 36 - subspace 9 adjoint operator 121 dense 102 admissible topology 65 dimension 2, 102 algebraic multiplicity 29 diminishing operator 162 alternating extension 115 direct sum (of operators) 30 - maximal pair 115 - sum (of subspaces) 2 - pair 114 dissipative operator 116 angular operator 54 domain 28 anti-space 6 doubly strict plus-operator 158 augmenting operator 162 dual companion (for a subspace) 21 companion (for a system) 21 Banach space with a J-metric 119 pair (of subspaces) 21 - topology 59 pair (of systems) 21 basis 2 cartesian product 8 eigenspace 29 Cayley transform 39 eigenvalue (of a quadratic pencil) 172 - transformation 39 - (of an operator) 29 closed (set) 102 - in a subspace 30 - operator 121 eigenvector 29 closure (of a set) 102 elementary solution 172 - (of an operator) 121 equivalent semi-norms 59 co dimension 3, 102 commuting operators 30 Frechet topology 59 compact operator 120 fundamental decomposition 24 - set 120 - projector 50 complementary subspace 2 - symmetry 52 complete system 82 fundamentally reducible operator 163 completely invertible operator 29 continuous 102 Gram operator 89 - spectrum 121 graph 121 222 Index of Terms
Hilbert topology 59 maximal definite subspace 12 homeomorphic 102 dissipative operator 117 hypermaximal neutral 5U bspace 15 negative definite subspace 'l2 negative subspace 12 identity operator 28 neutral subspace 12 indefinite inner product 4 non-degenerate subspace 12 - inner product space 4 positive definite subspace 'l2 - subspace 5 positive subspace 12 induced operator 30 rectangular isometric operator 128 - topology 59 semi-definite subspace 12 inner product 3 uniformly negative subspace 112 - product space 3 uniformly positive subspace 112 - square 4 minimalmajorant 84 intrinsic completion 71 - unitary dilation 139 dimension 71 - norm 71 natural norm 102 - topology 71 negative definite inner product 5 intrinsically complete 71 definite inner product space 5 invariant subspace 29 definite subspace 6 inverse operator 29 inner product 5 invertible operator 29 inner product space isometric operator 31 subspace 6 isometrical isomorphism 4 vector 4 isometrically isomorphic 4 neutral inner product 5 isomorphic 1 inner product space 5 isomorphism 1 part 4 isotropic part 9 set 4 - vector 9 subspace 6 vector 4 I-adjoint 122 non-strict plus-operator 46 I-inner product 52 non-uniformly definite subspace 109 I-isometric operator, normal eigenvalue 121 see A-isometric operator normed topology 59 I-norm 53 null space (of an operator) 28 I -orthogonal, see A -orthogonal operator matrix 30 - companion, ortho-complemented 18 orthogonal 7 see A -orthogonal companion I-symmetric operator, companion 7 see A-symmetric operator direct sum 7 Jordan chain (of a quadratic pencil) 172 projector 36 - chain (of an operator) 29 sum 7 orthonormal system 81 Krein space 100 partial majorant 59 length (of a Jordan chain) 29 Pesonen operator 48 linear form 28 plus-defect (of a subspace) 107 - operator 28 - (of an operator) 157 linearly independent subspaces 2 plus-operator 45 - independent vectors 2 point spectrum (of a quadratic pencil) locally convex topology 58 172 - spectrum (of an operator) 121 Mackey topology 96 polar (of a norm) 64 majorant 77 - (of a topology) 64 Index of Terms 223 polarization formula 4 second orthogonal companion 7 Pontrjagin space 184 selfadjoint operator 133 positive definite inner product self-polar topology 65 definite inner product space semi-definite inner product definite subspace 6 - inner product space inner product 5 - subspace 6 inner product space 5 semi-norm 58 operator 147 semi-simple eigenvalue 29 subspace 6 separable topology 59 vector 4 separated topology 59 positizabJe operator 180 singular subspace 71 positizing polynomial 180 span 1 principal subspace 29 spectral function 178, 180 - vector 29 spectrum (of a quadratic pencil) 174 proj ection 1 5 - (of an operator) 121 strict plus-operator 46 quadratic pencil 172 strong topology 102 - semi-norm 58 stronger (topology) 59 quadratic-normed topology 59 strongly damped 183 quasi-A-positive inner product 36 subspace 1 - inner product space 36 symmetric operator 34 quasi-negative inner product 25 - inner product space 25 topology defined by semi-norms 58 quasi-positive inner product 25 - inner product space 25 uniformly definite subspace 108 quotient space 3, 11 negative subspace 107 range 28 positive operator 151 rank (of an operator) 28 positive subspace 107 of A-negativity 149 unimodular number 31 of A-positivity 149 unitary dilation 139 of indefiniteness 95 - operator 128 of negativity 51, 95 of positivity 51, 95 vector space rectangular isometric operator 128 - sum 2 rcducing direct decomposition 30 regular point (of an operator) 121 weak operator topology 120 - subspace 71 - topology 60 - symmetric extension 197 weaker (topology) 59 residual spectrum 121 weakest majorant 87 resolvent set (of a quadratic pcncil) 174 - set (of an operator) 121 zero operator 28 restriction (of an operator) 30 - subspace 1 Index of Symbols
IAI 140 ~~+ 36 <~{>,
1. Bachmann: Transfinite ZaWen. DM 48,- 2. Miranda: Partial Differential Equations of Elliptic Type. DM 58,- 4. Samuel: Methodes d' Algebre Abstraite en Geometrie Algebrique. DM 34,- 5. Dieudonne: La Geometrie des Groupes Classiques. DM 42,- 7. Ostmann: Additive ZaWentheorie. 1. Teil: Allgemeine Untersuchungen. DM 42,- 8. \Vittich: Neuere Untersuchungen tiber eindeutige analytische Funktionen. DM 36,- 11. Ostmann: Additive Zahlentheorie. 2. Teil: Spezielle Zahlenmengen. DM 34,- 13. Segre: Some Properties of Differentiable Varieties and Transformations. DM 46,- 14. Coxeter/Moser: Generators and Relations for Discrete Groups 3rd edition. DM 42,- 15. Zeller/Beckmann: Theorie del' Limitierungsverfahren. DM 64,- 16. Cesari: Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. DM 54,- 17. Severi: II teorema di Riemann-Roch per curve, superficic e varieta questioni collegate. DM 30,- 18. Jenkins: Univalent Functions and Conformal Mapping. DM 37,- 19. Boas/Buck: Polynomial Expansions of Analytic Functions. DM 24,- 20. Bruck: A Survey of Binary Systems. DM 46,- 21. Day: Normed Linear Spaces. 3rd edition. DM 42,- 23. Bergmann: Integral Operators in the Theory of Linear Partial Differential Equations. DM 40,- 25. Sikorski: Boolean Algebras. DM 42,- 26. Ktinzi: Quasikonforme Abbildungen. DM 43,- 27. Schatten: Norm Ideals of Completely Continuous Operators. DM 30,- 28. Beckenbach/Bellmann: Inequalities. DM 38,- 29. vVolfowitz: Coding Theorems of Information Theory. DM 30,- 30. Constantinescu/Cornea: Ideale Randel' Riemannscher Flachen. DM 75,- 31. Conner/Floyd: Differentiable Periodic Maps. DM 34,- 32. Mumford: Geometric Invariant Theory. DM 24,- 33. Gabriel/Zisman: Calculus of Fractions and Homotopy Theory. DM 42,- 34. Putnam: Commutation Properties of Hilbert Space Operators and Related Topics. DM 31,- 35. Neumann: Varieties of Groups. DM 51,- 36. Boas: Integrability Theorems for Trigonometric Transforms. DM 20,- 37. Sz.-Nagy: Spektraldarstellung linearer Transformationen des Hilbertschen Raumes. DM 24,- 38. Seligman: Modular Lie Algebras. DlVI 43,- 39. Deuring: AIgebrcn. DM 30,- 40. Schutte: Vollstandige Systeme modaler und intuitionistischer Logik. DlVI 30,- 41. Smullyan: First-Order Logic. DM 36,- 42. Dembowski: Finite Geometries. DM 68,- 43. Linnik: Ergodic Properties of Algebraic Fields. DM 44,- 44. Krull: Idealtheorie. DM 34,- 45. Nachbin: Topology on Spaces of Holomorphic Mappings. DM 18,- 46. A. Ionescu Tulcea/C. Ionescu Tulcea: Topics in the Theory of Lifting. DM 36,- 47. Hayes/Pauc: Derivation and Martingales. DM 48,- 48. Kahane: Series de Fourier absolument convergentes. DM 44,- 49. Behnke/Thullen: Theorie der Funktionen mehrerer komplexer Veranderlichen. DM 48,- 50. Wilf: Finite Sections of Some Classical Inequalities. DM 28,- 51. Ramis: Sous-ensembles analytiques d'une variete banachique complexe. DM 36,- 52. Busemann: Recent Synthetic Differential Geometry. DM 32,- 53. Walter: Differential and Integral Inequalities. DM 74,- 54. Monna: Analyse non-archimedienne. DM 38,- 55. Alfsen: Compact Convex Sets and Boundary Integrals. DM 46,- 56. Greco/Salmon: Topics in m-Adic Topologies. DM 24,- 57. Lopez de Medrano: Involutions on Manifolds. DM 36,- 58. Sakai: C*-Algebras and W*-Algebras. DM 68,- 59· Zariski: Algebraic Surfaces. DM 54,- 60. Robinson: Finiteness Conditions and Generalized Soluble Groups, Part 1. DM 48,- 61. Robinson: Finiteness Conditions and Generalized Soluble Groups, Part 2. DM 64,- 62. Hakim: Topos anneles et schemas relatifs. DM 48,- 63. Browder: Surgery on Simply-Connected Manifolds. DM 42,- 64. Pietsch: Nuclear Locally Convex Spaces. DM 48,- 65. Dellacherie: Capacites et processus stochastiques. DM 44,- 66. Raghunathan: Discrete Subgroups of Lie Groups. DM 56,- 67. Rourke/Sanderson: Introduction to Piecewise-Linear Topology. DM 42,- 68. Kobayashi: Transformation Groups in Differential Geometry. DM 52,- 69. Tougeron: Ideaux de fonctions differentiables. DM 69,- 70. Gihman/Skorohod: Stochastic Differential Equations. DM 88,- 71. MilnorjHusemoller: Symmetric Bilinear Forms. DM 42,- 72. Fossum: The Divisor Class Group of a Krull Domain. DM 44,- 73. Springer: Jordan Algebras and Algebraic Groups. DM 48,- 74. Wehrfritz: Infinite Linear Groups. DM 59,- 75. Radjavi/Rosenthal: Invariant Subspaces. DM 50,- 76. Bognar: Indefinite Inner Product Spaces. DM 48,- 77. Skorohod: Integration in Hilbert Space. In preparation 78. Bonsall/Duncan: Complete Normed Algebras. DM 68,-