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
... of T is contained in the rectifiable Jordan curve To . Moreover , there is an integer valued function v defined on ... for T. An interval of constancy relative to T is a non - void open subinterval of г upon which some index function for ...
... of T is contained in the rectifiable Jordan curve To . Moreover , there is an integer valued function v defined on ... for T. An interval of constancy relative to T is a non - void open subinterval of г upon which some index function for ...
Page 2159
... in ( T ) . It follows that every Borel subset of To is measurable T. By Lemma 3.9 every subset of p ( T ) is in ( T ) and hence in a set measurable T. Thus , since σ ( T ) ≤ Ã 。, every Borel set in the plane is measurable T. Q.E.D. In ...
... in ( T ) . It follows that every Borel subset of To is measurable T. By Lemma 3.9 every subset of p ( T ) is in ( T ) and hence in a set measurable T. Thus , since σ ( T ) ≤ Ã 。, every Borel set in the plane is measurable T. Q.E.D. In ...
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 。 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 。 in an interval of constancy relative to T is ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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