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 1983
... Lebesgue measurable sets and ds is Lebesgue measure . The operators in the non - commutative B * -algebra Ao are then the operators A in H3 = L2 ( RN ) + ··· + L2 ( RN ) whose matrix representa- tion A = ( a ) consists of convolution ...
... Lebesgue measurable sets and ds is Lebesgue measure . The operators in the non - commutative B * -algebra Ao are then the operators A in H3 = L2 ( RN ) + ··· + L2 ( RN ) whose matrix representa- tion A = ( a ) consists of convolution ...
Page 2409
... Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let be an arbitrary complex B - space , and can consider the space L2 ( D , X ) of X - valued Borel - Lebesgue measurable functions defined in D. ( b ) We may ...
... Lebesgue measurable functions defined in D and satisfying ( 7 ) , we may let be an arbitrary complex B - space , and can consider the space L2 ( D , X ) of X - valued Borel - Lebesgue measurable functions defined in D. ( b ) We may ...
Page 2410
... Lebesgue measurable function defined in D × D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || = sup | A ( z , z ' ) | < ∞ , 2,2'ED and let ( 4 ) be the integral operator defined by the ...
... Lebesgue measurable function defined in D × D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || = sup | A ( z , z ' ) | < ∞ , 2,2'ED and let ( 4 ) be the integral operator defined by the ...
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