Linear Operators: General theory |
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Page xiv
... Spectral Operators XVI . Spectral Operators : Sufficient Conditions XVII . Algebras of Spectral Operators XVIII . Unbounded Spectral Operators XIX . Perturbations of Spectral Operators with Discrete Spectra XX . Perturbations of ...
... Spectral Operators XVI . Spectral Operators : Sufficient Conditions XVII . Algebras of Spectral Operators XVIII . Unbounded Spectral Operators XIX . Perturbations of Spectral Operators with Discrete Spectra XX . Perturbations of ...
Page 574
... spectral set of f ( T ) . Then o ( T ) f1 ( t ) is a spectral set of T , and = E ( t ; f ( T ) ) = E ( f − 1 ( t ) ; T ) . PROOF . Let e ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for u in a neighborhood of the rest ...
... spectral set of f ( T ) . Then o ( T ) f1 ( t ) is a spectral set of T , and = E ( t ; f ( T ) ) = E ( f − 1 ( t ) ; T ) . PROOF . Let e ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for u in a neighborhood of the rest ...
Page 761
... spectral properties of normal operators . Acta Sci . Math . Szeged 12 Pars B , 153–156 ( 1950 ) . Measurable transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. Van Nostrand , New York , 1950 ...
... spectral properties of normal operators . Acta Sci . Math . Szeged 12 Pars B , 153–156 ( 1950 ) . Measurable transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . Measure Theory . D. Van Nostrand , New York , 1950 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ