Linear Operators: Spectral operators |
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Results 1-3 of 97
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 + 10 and so T 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 X for which Ax = 0 is a closed left ideal ...
... Corollary 6 that NP + 10 and so T 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 X for which Ax = 0 is a closed left ideal ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero