Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 54
Page 2194
... algebra of all operators of the form Sƒ ( A ) 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 Sƒ ( A ) 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 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero