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 2068
... satisfies ( 11 ) . Also the space Lo grable functions which coincide almost everywhere function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L11 satisfies ( 11 ) . More generally , for any p with 1 ≤ p ≤oo , the ...
... satisfies ( 11 ) . Also the space Lo grable functions which coincide almost everywhere function clearly satisfies ( 11 ) . Example 11.12 shows that the space Lo L11 satisfies ( 11 ) . More generally , for any p with 1 ≤ p ≤oo , the ...
Page 2112
... satisfies the condition : ( α ) N ( F1 , T ) M ( F2 , T ) , if F the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X admits ...
... satisfies the condition : ( α ) N ( F1 , T ) M ( F2 , T ) , if F the interior of F2 , then T does admit such a duality theory . It is a distinctly non - trivial fact that every bounded linear operator T in a reflexive B - space X admits ...
Page 2399
... satisfies To2 = 0 , and also satisfies the second of the above asymptotic relationships . Hence , if we let o2 ( t ) be the unique solution 7σ2 = 0 such that σ2 ( t ) = 2 ( t ) for a too , our lemma is proved . Q.E.D. 14 COROLLARY ...
... satisfies To2 = 0 , and also satisfies the second of the above asymptotic relationships . Hence , if we let o2 ( t ) be the unique solution 7σ2 = 0 such that σ2 ( t ) = 2 ( t ) for a too , our lemma is proved . Q.E.D. 14 COROLLARY ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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