Linear operators: Spectral operators |
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Page 2194
Strongly Closed Algebras and Complete Boolean Algebras In this section an
attempt will be made to characterize the strong ... Let B be a bounded Boolean
algebra of projection operators in a weakly complete B-space X. Then the weakly
(or, ...
Strongly Closed Algebras and Complete Boolean Algebras In this section an
attempt will be made to characterize the strong ... Let B be a bounded Boolean
algebra of projection operators in a weakly complete B-space X. Then the weakly
(or, ...
Page 2214
Let B be a bounded Boolean algebra of projections in a 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 ...
Let B be a bounded Boolean algebra of projections in a 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 ...
Page 2218
as the weakly closed operator algebra generated by B) is the same as the
uniformly closed operator algebra ... a generalized sequence of projections in a a
-complete Boolean algebra of projections in a B-space converges weakly to a ...
as the weakly closed operator algebra generated by B) is the same as the
uniformly closed operator algebra ... a generalized sequence of projections in a a
-complete Boolean algebra of projections in a B-space converges weakly to a ...
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Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
47 other sections not shown
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adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero