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 ( \ ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full ... 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 - essentially bounded on o ( S ) . It follows from Theorem 10 that A1 is a full ... ALGEBRAS OF SPECTRAL OPERATORS Strongly Closed Algebras and Complete Boolean Algebras.
Page 2195
... Boolean algebra B of projections in a B - space X is said to be complete ( o - complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a greatest lower bound and a least upper bound in B. The Boolean algebra B is ...
... Boolean algebra B of projections in a B - space X is said to be complete ( o - complete ) as an abstract Boolean algebra if each subset ( sequence ) of B has a greatest lower bound and a least upper bound in B. The Boolean algebra B is ...
Page 2217
... Boolean algebra of projections in a B - space X , and let B1 be its strong closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a ...
... Boolean algebra of projections in a B - space X , and let B1 be its strong closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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