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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Results 1-3 of 21
Page 1951
... compact , then so are S , N , and every projection E ( o ) with 0 ₫ ō . PROOF . By Corollary VI.4.6 the weakly compact operators form a closed two - sided ideal in B ( X ) , from which the present statement follows . Q.E.D. If is a ...
... compact , then so are S , N , and every projection E ( o ) with 0 ₫ ō . PROOF . By Corollary VI.4.6 the weakly compact operators form a closed two - sided ideal in B ( X ) , from which the present statement follows . Q.E.D. If is a ...
Page 2110
... weakly compact subsets are compact ( for example , 1 ) . Thus the scalar operators in such spaces are limits in the strong operator topology of finite dimensional operators . Since some interesting non - normable locally convex spaces ...
... weakly compact subsets are compact ( for example , 1 ) . Thus the scalar operators in such spaces are limits in the strong operator topology of finite dimensional operators . Since some interesting non - normable locally convex spaces ...
Page 2186
... weakly complete space is weakly compact ( cf. VI.7.6 ) , it is seen from Theorem VI.7.3 that the map f → S ( f ) x uniquely determines a regular X - valued measure v ( · , x ) such that ( i ) S ( ƒ ) x = √ ƒ ( \ ) v ( dλ , x ) , ƒЄ C ...
... weakly complete space is weakly compact ( cf. VI.7.6 ) , it is seen from Theorem VI.7.3 that the map f → S ( f ) x uniquely determines a regular X - valued measure v ( · , x ) such that ( i ) S ( ƒ ) x = √ ƒ ( \ ) v ( dλ , x ) , ƒЄ C ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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