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 41
Page 2194
... Complete Boolean Algebras In this section an attempt will be made to ... weakly ) closed operator algebra generated by 7. The following discussion ... weakly complete B - space X. Then the weakly ( or , equivalently , strongly ) closed ...
... Complete Boolean Algebras In this section an attempt will be made to ... weakly ) closed operator algebra generated by 7. The following discussion ... weakly complete B - space X. Then the weakly ( or , equivalently , strongly ) closed ...
Page 2214
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
Page 2218
... weakly closed operator algebra generated by B ) is the same as the uniformly closed operator algebra generated by B1 ... complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly ...
... weakly closed operator algebra generated by B ) is the same as the uniformly closed operator algebra generated by B1 ... complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly ...
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