Linear Operators, Part 2 |
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Page 2118
... scalar operator T e 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 T e 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 p , 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 p , 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
... scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = λ ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions . Similarly , if X = L „ ( N ) , 1 ...
... scalar if there exists an A - spectral function U : A → B ( X ) such that SU11 ( where f1 ( A ) = λ ) . Every scalar type spectral operator is A - scalar , with the algebra of bounded Borel functions . Similarly , if X = L „ ( N ) , 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero