Linear Operators: Spectral operators |
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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 HP L2 ( RN ) + ··· + L2 ( RN ) whose matrix representa- Ho = tion A = ( αjk ) consists of ...
... Lebesgue measurable sets and ds is Lebesgue measure . The operators in the non - commutative B * -algebra Ao are then the operators A in HP L2 ( RN ) + ··· + L2 ( RN ) whose matrix representa- Ho = tion A = ( αjk ) consists of ...
Page 2407
... Lebesgue dominated convergence theorem we have lim , so that lim → ∞ | Ãh , —Ãh | q = 0 . By Fatou's lemma ( III.6.17 ) ( 21 ) lim С | A ( s , t ) | h , ( t ) μ ( dt ) = [ [ A ( s , t ) | h ( t ) μ ( dt ) n → ∞ hnh | q = 0 , for ...
... Lebesgue dominated convergence theorem we have lim , so that lim → ∞ | Ãh , —Ãh | q = 0 . By Fatou's lemma ( III.6.17 ) ( 21 ) lim С | A ( s , t ) | h , ( t ) μ ( dt ) = [ [ A ( s , t ) | h ( t ) μ ( dt ) n → ∞ hnh | q = 0 , for ...
Page 2410
... Lebesgue measurable function defined in D x 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 ( A ) be the integral operator defined by the equation ...
... Lebesgue measurable function defined in D x 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 ( A ) be the integral operator defined by the equation ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero