Linear Operators: Spectral operators |
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Page 2118
... scalar operator Te B ( X ) is said to be regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given ...
... scalar operator Te B ( X ) is said to be regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given ...
Page 2119
... scalar operator with spectrum contained in the image , under 9 , of the support of U. In particular , if T is a generalized scalar operator and U is a spectral distribution for T , then o ( T ) coincides with the sup- port of U. In ...
... scalar operator with spectrum contained in the image , under 9 , of the support of U. In particular , if T is a generalized scalar operator and U is a spectral distribution for T , then o ( T ) coincides with the sup- port of U. In ...
Page 2120
... operator Se B ( X ) is called 2 - scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions ...
... operator Se B ( X ) is called 2 - scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions ...
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