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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Results 1-3 of 53
Page 1925
... normal ) operators as developed in Chapters X and XII . The problem of extending this reduction theory to non - normal operators is one of the most important unsolved problems in the theory of linear operations . Consider , for instance ...
... normal ) operators as developed in Chapters X and XII . The problem of extending this reduction theory to non - normal operators is one of the most important unsolved problems in the theory of linear operations . Consider , for instance ...
Page 1978
... normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p xp matrix  ( s ) is normal . Since , for a Borel set σ , the projection E = E ( σ ;  ...
... normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p xp matrix  ( s ) is normal . Since , for a Borel set σ , the projection E = E ( σ ;  ...
Page 2005
... normal operators . Thus both of the operators in ( 57 ) are scalar type operators , and for any a and b in 2 , they are similar to normal operators . In the case of the operators ( 55 ) and ( 58 ) the situation is somewhat different ...
... normal operators . Thus both of the operators in ( 57 ) are scalar type operators , and for any a and b in 2 , they are similar to normal operators . In the case of the operators ( 55 ) and ( 58 ) the situation is somewhat different ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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