Linear Operators: Spectral operators |
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Page 2013
... given by ( 9 ) and the domain of A consists precisely of those q for which the limit in ( 9 ) exists . Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
... given by ( 9 ) and the domain of A consists precisely of those q for which the limit in ( 9 ) exists . Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
Page 2096
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
Page 2376
... given , one attempts to find an operator U such that T + K = U - 1TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied with success to a wide variety of operators and , in ...
... given , one attempts to find an operator U such that T + K = U - 1TU , in this way reducing the spectral theory of T + K to that of T. We shall see that this idea can be applied with success to a wide variety of operators and , in ...
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