Linear Operators: Spectral operators |
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Page 2084
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T , ) E ( 0 ) | ≤ dist ( έ , ō ) m for § & ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T , ) E ( 0 ) | ≤ dist ( έ , ō ) m for § & ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
Page 2171
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
Page 2188
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then S g ( μ ) E ( f - 1 ( du ) ) , | _ g ( f ( x ) ) E ...
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then S g ( μ ) E ( f - 1 ( du ) ) , | _ g ( f ( x ) ) E ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero