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 ) f - 1 ( t ) is a spectral set of T , and = E ( t ; f ( T ) ) = E ( j - 1 ( t ) ; T ) . PROOF . Let e , ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for μ in a neighborhood of the ...
... spectral set of f ( T ) . Then o ( T ) f - 1 ( t ) is a spectral set of T , and = E ( t ; f ( T ) ) = E ( j - 1 ( t ) ; T ) . PROOF . Let e , ( u ) = 1 for u in a neighborhood of t , and let e ( u ) = 0 for μ in a neighborhood of the ...
Page 749
... Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . 8. Integration ... Spectral theory in abstract spaces and Banach algebras . Proc . Symposium on Spectral Theory and Differential ...
... Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . 8. Integration ... Spectral theory in abstract spaces and Banach algebras . Proc . Symposium on Spectral Theory and Differential ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ