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 2005
... operator A in A2 , not of the form A = AI with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
... operator A in A2 , not of the form A = AI with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
Page 2411
... operator T +4 ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . = REMARK . It follows from Theorem XII.3.16 that if To is any bounded normal operator in Hilbert space whose spectral resolution E ...
... operator T +4 ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . = REMARK . It follows from Theorem XII.3.16 that if To is any bounded normal operator in Hilbert space whose spectral resolution E ...
Page 2516
... operator . Amer . Math . Monthly 70 , 1049-1051 ( 1963 ) . A note on ... operator . Proc . Amer . Math . Soc . 18 , 499-503 ( 1967 ) . Berezanskii , Ju . M. ( Yu ... normal operators . J. London Math . Soc . 40 , 478-486 ( 1965 ) . The ...
... operator . Amer . Math . Monthly 70 , 1049-1051 ( 1963 ) . A note on ... operator . Proc . Amer . Math . Soc . 18 , 499-503 ( 1967 ) . Berezanskii , Ju . M. ( Yu ... normal operators . J. London Math . Soc . 40 , 478-486 ( 1965 ) . The ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 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