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 |
From inside the book
Results 1-3 of 59
Page 2194
... algebra of all operators of the form ƒ ƒ ( \ ) 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 ( \ ) 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 4 of maximal ideals in A ( 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 4 of maximal ideals in A ( 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 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero