Linear Operators: Spectral operators |
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Page 2118
... regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any two regular spectral distributions U ...
... regular if it has a regular spectral distribution . Although it is not known whether or not every generalized scalar operator is regular ( unless the spectrum is sufficiently " thin " ) , given any two regular spectral distributions U ...
Page 2158
... regular relative to T is dense on To , then every closed subinterval of T。 whose end points are regular relative to T is in ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let y be a closed subinterval of 。 whose ...
... regular relative to T is dense on To , then every closed subinterval of T。 whose end points are regular relative to T is in ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let y be a closed subinterval of 。 whose ...
Page 2160
... regular points relative 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 ...
... regular points relative 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 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero