Linear Operators, Part 2 |
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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 г。 whose end points are regular relative to T is in S ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let γ be a closed subinterval of To ...
... regular relative to T is dense on To , then every closed subinterval of г。 whose end points are regular relative to T is in S ( T ) and every Borel subset of the plane is measurable T. 0 PROOF . Let γ be a closed subinterval of To ...
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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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