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 2154
... on T。 such that for every λo in гo , | ( λ — λ 。) o ‹ 1o ) R ( λ ; T ) | ≤ 1 , λ λο , λε Διο In the analysis to ... for T. An interval of constancy relative to T is a non - void open subinterval of à 。 upon which some index function ...
... on T。 such that for every λo in гo , | ( λ — λ 。) o ‹ 1o ) R ( λ ; T ) | ≤ 1 , λ λο , λε Διο In the analysis to ... for T. An interval of constancy relative to T is a non - void open subinterval of à 。 upon which some index function ...
Page 2159
... to T are dense on T 。. Some results in this direction will be found in the next four lemmas . 11 LEMMA ( G ) . The union of all intervals of constancy relative to T is an open set dense in г. PROOF . It is clear that the union of ...
... to T are dense on T 。. Some results in this direction will be found in the next four lemmas . 11 LEMMA ( G ) . The union of all intervals of constancy relative to T is an open set dense in г. PROOF . It is clear that the union of ...
Page 2160
... to T are dense in To and , in particular , every interval of constancy relative to T consists entirely of regular points . PROOF . In view of Lemma 11 it suffices to show that a point λ in an interval of constancy relative to T is ...
... to T are dense in To and , in particular , every interval of constancy relative to T consists entirely of regular points . PROOF . In view of Lemma 11 it suffices to show that a point λ in an interval of constancy relative to T is ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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