Linear Operators: Spectral operators |
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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 Д. This means that for every Borel set e in Д 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 Д. This means that for every Borel set e in Д there is a projection E ( e ) in B with A ( e ) = E ( e ) ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
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