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 2013
... given by ( 9 ) and the domain of A consists precisely of those q for which the limit in ( 9 ) exists . σ Ф Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
... given by ( 9 ) and the domain of A consists precisely of those q for which the limit in ( 9 ) exists . σ Ф Our next concern will be with the question of the existence of a resolution of the identity for A. This leads us to formulate the ...
Page 2088
... given by equations 12.4 . Show that if A is a scalar type spectral operator whose spectrum lies in a left half plane then it is the infinitesimal generator of the strongly continuous semi - group T ( t ) , t≥ 0 , given by the equation ...
... given by equations 12.4 . Show that if A is a scalar type spectral operator whose spectrum lies in a left half plane then it is the infinitesimal generator of the strongly continuous semi - group T ( t ) , t≥ 0 , given by the equation ...
Page 2096
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
... given , based on a theorem which asserts that , under certain hypotheses , a continuous linear mapping U of a Banach algebra A with unit e into B ( X ) is the projection of a continuous homomorphism of A into B ( X ) for some B - space ...
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