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 2111
... weak T - measure and each x * = X * has a weak T * -1 -measure . The main results in Bishop [ 1 ] are extended to a locally convex space which is barreled and quasi - complete by Maeda [ 1 , 2 ] . Bishop's " duality theories . " In a ...
... weak T - measure and each x * = X * has a weak T * -1 -measure . The main results in Bishop [ 1 ] are extended to a locally convex space which is barreled and quasi - complete by Maeda [ 1 , 2 ] . Bishop's " duality theories . " In a ...
Page 2194
... weak as in the 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 ...
... weak as in the 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 ...
Page 2281
... weaker form of completeness enjoyed by B * leads to a weaker form of the representation theorem , as the relevant topology ... weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of ...
... weaker form of completeness enjoyed by B * leads to a weaker form of the representation theorem , as the relevant topology ... weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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