Linear Operators: Spectral operators |
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Page 2125
... limit , we obtain a g.s.m. Po on D。( P ) which extends P and which is maxi- mal in a certain technical sense . = Let be the set of elements xЄH such that x = P ( S ) x for some SE D ( P ) ; Ljance calls the space of basic elements ...
... limit , we obtain a g.s.m. Po on D。( P ) which extends P and which is maxi- mal in a certain technical sense . = Let be the set of elements xЄH such that x = P ( S ) x for some SE D ( P ) ; Ljance calls the space of basic elements ...
Page 2219
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim Tα of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim Tα of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
Page 2454
... limit as t → ∞ if and only if U ( 3.2 ) x ' has a it follows that limit as too , Q.E.D. and that , if either limit exists , both limits are equal . 4 COROLLARY . Let H1 and H2 be two self 2454 XX.4.1 SPECTRAL OPERATORS WITH CONTINUOUS ...
... limit as t → ∞ if and only if U ( 3.2 ) x ' has a it follows that limit as too , Q.E.D. and that , if either limit exists , both limits are equal . 4 COROLLARY . Let H1 and H2 be two self 2454 XX.4.1 SPECTRAL OPERATORS WITH CONTINUOUS ...
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