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
... reflexive B - space X is a spectral operator if and only if each xe X has 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 ...
... reflexive B - space X is a spectral operator if and only if each xe X has 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 ...
Page 2161
... reflexive , it follows from the Hahn- Banach theorem ( cf. Corollary II.3.13 ) that there is an x in X with x * x 0 ... reflexive and the function v ( λ ) = 1 , λεΓο , is an index function for the operator . ( c ) The space is reflexive ...
... reflexive , it follows from the Hahn- Banach theorem ( cf. Corollary II.3.13 ) that there is an x in X with x * x 0 ... reflexive and the function v ( λ ) = 1 , λεΓο , is an index function for the operator . ( c ) The space is reflexive ...
Page 2174
... reflexive . To see this , note that if S and T are commuting scalar operators with real spectrum then lettsM , and lettr≤ M2 for all te R. Hence we have 1 2 lett ( S + T ) | = | ettsettT | ≤etts || ettr≤ M1M2 1 for all te R. Hence if ...
... reflexive . To see this , note that if S and T are commuting scalar operators with real spectrum then lettsM , and lettr≤ M2 for all te R. Hence we have 1 2 lett ( S + T ) | = | ettsettT | ≤etts || ettr≤ M1M2 1 for all te R. Hence if ...
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