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 1915
... resolvent near the spectrum . Thus the reader whose pri- mary interest is in the applications to such topics as ... resolvent of T ' = T + P in terms of the resolvent of T , and from this to relate the spectral projections of T ' to ...
... resolvent near the spectrum . Thus the reader whose pri- mary interest is in the applications to such topics as ... resolvent of T ' = T + P in terms of the resolvent of T , and from this to relate the spectral projections of T ' to ...
Page 1931
... resolvent ( IT ) -1 of T at the point έ in the resolvent set p ( T ) . If x is a vector in X , then by an analytic extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) ≥ p ( T ) ...
... resolvent ( IT ) -1 of T at the point έ in the resolvent set p ( T ) . If x is a vector in X , then by an analytic extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) ≥ p ( T ) ...
Page 2291
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . - DEFINITION . An operator T is discrete if there is a number λ in its resolvent set ...
... resolvent occurs so frequently in this section , it will be convenient to introduce , in the following definition , a special term for such operators . - DEFINITION . An operator T is discrete if there is a number λ in its resolvent set ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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