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 2106
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then A2 is a scalar type operator . Moreover , if A is adjoint Abelian and X is weakly complete , then A is scalar type if and only if either ( a ) A is ...
Page 2174
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ettr | te R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
... scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded group G = { ettr | te R } is equivalent to a group of unitary operators . By Stone's theorem , the latter group has an infinitesi ...
Page 2218
... scalar type . Q.E.D. 26 COROLLARY . Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type ...
... scalar type . Q.E.D. 26 COROLLARY . Every operator in the weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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