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 ( -1 ( t ) ; T ) . PROOF . Let e , ( u ) = 1 for μ in a neighborhood of t , and let e ( u ) = 0 for u in a neighborhood of the rest of o ...
... spectral set of f ( T ) . Then o ( T ) f1 ( T ) is a spectral set of T , and E ( t ; f ( T ) ) = E ( -1 ( t ) ; T ) . PROOF . Let e , ( u ) = 1 for μ in a neighborhood of t , and let e ( u ) = 0 for u in a neighborhood of the rest of o ...
Page 749
... Spectral theory . Bull . Amer . Math . Soc . 49 , 637-651 ( 1943 ) . 7 . Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . 8 ... Spectral theory . Proc . Symposium on Spectral REFERENCES 749.
... Spectral theory . Bull . Amer . Math . Soc . 49 , 637-651 ( 1943 ) . 7 . Spectral theory I , Convergence to projections . Trans . Amer . Math . Soc . 54 , 185-217 ( 1943 ) . 8 ... Spectral theory . Proc . Symposium on Spectral REFERENCES 749.
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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ