Linear Operators: Spectral operators |
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Page 2118
... scalar operator T € 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 € 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 q , 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 q , 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 A - scalar if there exists an A - spectral function . U : A → B ( X ) such that S = U11 ( where fi ( A ) = λ ) . Every scalar type spectral operator is 2 - scalar , with the algebra of bounded Borel ...
... operator SE B ( X ) is called A - scalar if there exists an A - spectral function . U : A → B ( X ) such that S = U11 ( where fi ( A ) = λ ) . Every scalar type spectral operator is 2 - scalar , with the algebra of bounded Borel ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero