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 p for which the limit Ф in ( 9 ) exists . 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 p for which the limit Ф in ( 9 ) exists . 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 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero