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 83
Page 1951
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ₫ ō . PROOF ...
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ₫ ō . PROOF ...
Page 1952
... Corollary 6 that NP + 1 is of finite type . Q.E.D. ¢ 8 COROLLARY . If Tx = 0 , then Sx = Nx = E ( o ) x = 0 if 0 ₫ ō . PROOF . For a given x in X , the class of bounded linear operators in for which Ax = 0 is a closed left ideal in B ...
... Corollary 6 that NP + 1 is of finite type . Q.E.D. ¢ 8 COROLLARY . If Tx = 0 , then Sx = Nx = E ( o ) x = 0 if 0 ₫ ō . PROOF . For a given x in X , the class of bounded linear operators in for which Ax = 0 is a closed left ideal in B ...
Page 2192
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
Contents
SPECTRAL OPERATORS | 1924 |
The Algebras A and | 1966 |
Some Examples of Bounded Spectral Operators | 1983 |
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