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 2194
... algebra of all operators of the form ƒ ƒ ( λ ) E ( dλ ) where ƒ is E ... projections in its resolution of the identity , the problem of the present ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
... algebra of all operators of the form ƒ ƒ ( λ ) E ( dλ ) where ƒ is E ... projections in its resolution of the identity , the problem of the present ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
Page 2199
... algebra A ( B ) generated by the projections in B. By Lemma 2.1 the algebra ( B ) is equivalent , under an isomorphism S ( f ) → f , to the algebra C ( 4 ) of continuous functions on the space △ of maximal ideals in ( B ) . Moreover ...
... algebra A ( B ) generated by the projections in B. By Lemma 2.1 the algebra ( B ) is equivalent , under an isomorphism S ( f ) → f , to the algebra C ( 4 ) of continuous functions on the space △ of maximal ideals in ( B ) . Moreover ...
Page 2218
... 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 . PROOF . Since a spectral operator of scalar type is clearly in the weakly closed algebra ...
... 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 . PROOF . Since a spectral operator of scalar type is clearly in the weakly closed algebra ...
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