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 2094
... moreover , if T * is spectral of class ( Ã ) where г ≤ X ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( T ) , then T has a unique resolution of the identity ...
... moreover , if T * is spectral of class ( Ã ) where г ≤ X ** , then it has a unique resolution of the identity of class ( Ã ) . If X * is weakly complete and T is spectral of class ( T ) , then T has a unique resolution of the identity ...
Page 2183
... Moreover , P is evidently a projection in B. - The set B is clearly a subalgebra of A ( 7 ) . Let B denote its closure in the uniform topology of operators . By Theorem XV.4.5 and the fact that a scalar type operator is clearly in the ...
... Moreover , P is evidently a projection in B. - The set B is clearly a subalgebra of A ( 7 ) . Let B denote its closure in the uniform topology of operators . By Theorem XV.4.5 and the fact that a scalar type operator is clearly in the ...
Page 2470
... Moreover , by this same lemma , we have ( 49 ) | T | 2 = Σ ̧ ƒ ƒ | L , ( a , b ) | 2 μ ( da ) μ ( db ) . i , j = 1 R Using ( 48 ) and the fact that fi ( a ) = 0 for a Єe ,, we have + ∞ + ∞ n ( 50 ) | Te } | 2 dt = ↓ | £ § L. , ( a ...
... Moreover , by this same lemma , we have ( 49 ) | T | 2 = Σ ̧ ƒ ƒ | L , ( a , b ) | 2 μ ( da ) μ ( db ) . i , j = 1 R Using ( 48 ) and the fact that fi ( a ) = 0 for a Єe ,, we have + ∞ + ∞ n ( 50 ) | Te } | 2 dt = ↓ | £ § L. , ( a ...
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