Linear Operators, Part 2 |
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Results 1-3 of 90
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. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ‡ ō ...
... 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. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ‡ ō ...
Page 1952
... Corollary 6 that NP + 1 = 0 and so T say is of finite type . T , - 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 X for which Ax = 0 is a ...
... Corollary 6 that NP + 1 = 0 and so T say is of finite type . T , - 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 X for which Ax = 0 is a ...
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 Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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