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 2111
... reflexive B - space X is a spectral operator if and only if each xex has a weak T - measure and each x * Є X * has a weak T * -measure . The main results in Bishop [ 1 ] are extended to a locally convex space which is barreled and quasi ...
... reflexive B - space X is a spectral operator if and only if each xex has a weak T - measure and each x * Є X * has a weak T * -measure . The main results in Bishop [ 1 ] are extended to a locally convex space which is barreled and quasi ...
Page 2161
... reflexive , it follows from the Hahn- Banach theorem ( cf. Corollary II.3.13 ) that there is an x in X with x * x 0 ... reflexive and the function v ( λ ) = 1 , λεΓο , is an index function for the operator . ( c ) The space is reflexive ...
... reflexive , it follows from the Hahn- Banach theorem ( cf. Corollary II.3.13 ) that there is an x in X with x * x 0 ... reflexive and the function v ( λ ) = 1 , λεΓο , is an index function for the operator . ( c ) The space is reflexive ...
Page 2176
... reflexive B - space , Lorch was able to construct for each 0 E [ 0,2 ] a pair ( E. , F. ) of closed subspaces which are invariant under T and which resemble the manifolds corresponding to a resolution of the identity . Alternatively ...
... reflexive B - space , Lorch was able to construct for each 0 E [ 0,2 ] a pair ( E. , F. ) of closed subspaces which are invariant under T and which resemble the manifolds corresponding to a resolution of the identity . Alternatively ...
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