Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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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 2403
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) D ↓↓ 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | | f ( z ) | 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 ( A1 ) ...
... theorem ( III.11.14 ) , the integral ( 75 ) D ↓↓ 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | | f ( z ) | 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 ( A1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero