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 1989
... measure in H , and thus , since F is unitary , the measure e ( o ) , σ € Σ , is a spectral measure with these same properties . We also have e ( σ ) = 0 if and only if o has Lebesgue measure zero so that the notions of e - almost ...
... measure in H , and thus , since F is unitary , the measure e ( o ) , σ € Σ , is a spectral measure with these same properties . We also have e ( σ ) = 0 if and only if o has Lebesgue measure zero so that the notions of e - almost ...
Page 2110
... measure into the space of con- μ tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
... measure into the space of con- μ tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
Page 2111
... measure of x . However , not every operator has a non - trivial T - measure ; consider the right shift operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes ...
... measure of x . However , not every operator has a non - trivial T - measure ; consider the right shift operator in l2 , or a quasi- nilpotent operator with empty point spectrum . It is proved that if m is a T - measure , then m vanishes ...
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