Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1938
... scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which satisfies the equation S = √ λE ( dλ ) , Ε where E is the resolution ...
... scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which satisfies the equation S = √ λE ( dλ ) , Ε where E is the resolution ...
Page 2106
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator ... Spectral operators and unconditional convergence . If T is a scalar type operator whose eigenvectors are a fundamental set ...
... scalar type operator of class ( X ) , and ( ii ) if x is weakly complete , then 42 is a scalar type operator ... Spectral operators and unconditional convergence . If T is a scalar type operator whose eigenvectors are a fundamental set ...
Page 2174
... scalar operator ; on the other hand , Krabbe [ 6 ] shows that although certain convolution operators are not spectral ... type operator with real spectrum . ( This follows from Lemma XV.6.1 which ... spectral , even when X is reflexive . To see ...
... scalar operator ; on the other hand , Krabbe [ 6 ] shows that although certain convolution operators are not spectral ... type operator with real spectrum . ( This follows from Lemma XV.6.1 which ... spectral , even when X is reflexive . To see ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions 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 E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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