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 74
Page 2300
... uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σ- , ( E ( \ , ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K ...
... uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σ- , ( E ( \ , ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K ...
Page 2347
... uniformly bounded . An equivalent norm in H ( 0 , 1 ) is ( iv ) 1 1/2 = dt + 1/2 0 0 The family ( iii ) of maps is evidently uniformly bounded as a set of maps of L2 ( 0 , 1 ) into itself . Consequently , it suffices to show ( using the ...
... uniformly bounded . An equivalent norm in H ( 0 , 1 ) is ( iv ) 1 1/2 = dt + 1/2 0 0 The family ( iii ) of maps is evidently uniformly bounded as a set of maps of L2 ( 0 , 1 ) into itself . Consequently , it suffices to show ( using the ...
Page 2361
... bounded domains covering the whole complex plane , and suppose that lim ̧ → ∞ min2e u1 | 2 = ∞ . Let V , be the ... uniformly bounded for each fe ∞ ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was ...
... bounded domains covering the whole complex plane , and suppose that lim ̧ → ∞ min2e u1 | 2 = ∞ . Let V , be the ... uniformly bounded for each fe ∞ ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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