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 2248
... THEOREM . Let T be a spectral operator , and E its resolution of identity . Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a neighborhood of o ( T ) and a ...
... THEOREM . Let T be a spectral operator , and E its resolution of identity . Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a neighborhood of o ( T ) and a ...
Page 2283
... theorem . → 32 THEOREM . Let B be a complete Boolean algebra of projections in a Banach space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E in B has finite uniform multiplicity n if and only if its ...
... theorem . → 32 THEOREM . Let B be a complete Boolean algebra of projections in a Banach space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E in B has finite uniform multiplicity n if and only if its ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero