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 - 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 ( λ ) 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 |
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