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 2113
... Foiaş [ 12 ] and Colojoară and Foiaş [ 1 , 4 ] . See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foias [ 2 , 5 ] , Kariotis [ 1 ] , and Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable operators . Let S ...
... Foiaş [ 12 ] and Colojoară and Foiaş [ 1 , 4 ] . See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foias [ 2 , 5 ] , Kariotis [ 1 ] , and Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable operators . Let S ...
Page 2129
... Foias [ 1 , 6 , 9 , 10 ] , Volk [ 1 ] , Wermer [ 1 , 2 , 4 ] . Contractions and dilations . On pages 931-932 we have briefly discussed contractions and dilations of operators in Hilbert space . This theory , which was sparked by some ...
... Foias [ 1 , 6 , 9 , 10 ] , Volk [ 1 ] , Wermer [ 1 , 2 , 4 ] . Contractions and dilations . On pages 931-932 we have briefly discussed contractions and dilations of operators in Hilbert space . This theory , which was sparked by some ...
Page 2509
... Foias [ 4 ] ) . The initial idea in this development is as follows . Let T be an operator in a B - space such that ... Foias [ 9 , 10 , 12 ] . The second of the above cited papers of Foiaş discusses the connection between the theory ...
... Foias [ 4 ] ) . The initial idea in this development is as follows . Let T be an operator in a B - space such that ... Foias [ 9 , 10 , 12 ] . The second of the above cited papers of Foiaş discusses the connection between the theory ...
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