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 58
Page 1984
... clearly a linear subset of all the Lebesgue spaces L , L , ( RN ) , 1≤poo , and , for p in Ø , the symbol = , is used for the norm of o as an element of L ,. Besides having topol- ogies as a subset of various B - spaces , the set Ø ...
... clearly a linear subset of all the Lebesgue spaces L , L , ( RN ) , 1≤poo , and , for p in Ø , the symbol = , is used for the norm of o as an element of L ,. Besides having topol- ogies as a subset of various B - spaces , the set Ø ...
Page 2183
... 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 uniformly closed algebra generated by the projections in its ...
... 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 uniformly closed algebra generated by the projections in its ...
Page 2267
... Clearly Exoxo . We assert E is the -Σ carrier of xo . For suppose that Fe B and Fxoxo . Then for each n , = n - = 2- " xnExo E2 Fx 。 FE2 xo = 2- " Fxn . Thus Fx , xn , n = 1 , 2 , that FE . Q.E.D. n showing FE ,, n = 1 , 2 , ... . It ...
... Clearly Exoxo . We assert E is the -Σ carrier of xo . For suppose that Fe B and Fxoxo . Then for each n , = n - = 2- " xnExo E2 Fx 。 FE2 xo = 2- " Fxn . Thus Fx , xn , n = 1 , 2 , that FE . Q.E.D. n showing FE ,, n = 1 , 2 , ... . It ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
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