Linear Operators: Spectral operators |
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Page 2162
... Theorem 4.5 , to prove the present theorem it suffices to show that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if the points regular relative to T are dense on T 。. Thus Lemmas 12 , 13 , 14 give the ...
... Theorem 4.5 , to prove the present theorem it suffices to show that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if the points regular relative to T are dense on T 。. Thus Lemmas 12 , 13 , 14 give the ...
Page 2249
... Theorem 9 ( v ) that ( 1 / f ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( f ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
... Theorem 9 ( v ) that ( 1 / f ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( f ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) SoS 142 ( 2 " , 2 ) | A2 ( z , z ' ) | z — x ' | | f ( x ' ) dx ' dy ' dx dy exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ...
... theorem ( III.11.14 ) , the integral ( 75 ) SoS 142 ( 2 " , 2 ) | A2 ( z , z ' ) | z — x ' | | f ( x ' ) dx ' dy ' dx dy exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ...
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