Linear Operators: Spectral operators |
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Page 2195
... 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 said to be complete ( o - complete ) if it is complete ( o ...
... 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 said to be complete ( o - complete ) if it is complete ( o ...
Page 2197
... complete ( o - complete ) Boolean algebra of pro- jections in the B - space X and let { E } be a monotone generalized sequence ( a monotone sequence ) in B. Then , if { E } is increasing , lim Ex = = ( V Eα ) x , x = X , α while if { E } ...
... complete ( o - complete ) Boolean algebra of pro- jections in the B - space X and let { E } be a monotone generalized sequence ( a monotone sequence ) in B. Then , if { E } is increasing , lim Ex = = ( V Eα ) x , x = X , α while if { E } ...
Page 2217
... complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B1 and an x in X such that the ... complete . Thus , by Corollary 7 , B ( x ) is not complete . On the other hand , B ( x ) is , according to Corollary 11 ...
... complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B1 and an x in X such that the ... complete . Thus , by Corollary 7 , B ( x ) is not complete . On the other hand , B ( x ) is , according to Corollary 11 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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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