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 2144
... topology of X * , and is bounded . It remains only to show that A ( o ) A ... operator in the weakly complete complex B - space X and let E be the associated ... strong operator topology . This extension is bounded and commutes with T ...
... topology of X * , and is bounded . It remains only to show that A ( o ) A ... operator in the weakly complete complex B - space X and let E be the associated ... strong operator topology . This extension is bounded and commutes with T ...
Page 2194
... strong operator topology . Thus the strong and weak operator closures of an algebra of operators are the same . This section , like the last one , starts with a commuting family of spectral operators together with their resolutions of ...
... strong operator topology . Thus the strong and weak operator closures of an algebra of operators are the same . This section , like the last one , starts with a commuting family of spectral operators together with their resolutions of ...
Page 2204
... strong operator topology . Thus x * Ex = xA ( e ) x * , which proves that e is in and shows that Σ consists of all Borel sets in 4. This means that for every Borel set e in 4 there is a projection E ( e ) in B with A ( e ) = E ( e ) ...
... strong operator topology . Thus x * Ex = xA ( e ) x * , which proves that e is in and shows that Σ consists of all Borel sets in 4. This means that for every Borel set e in 4 there is a projection E ( e ) in B with A ( e ) = E ( e ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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Common terms and phrases
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