Linear Operators: Spectral operators |
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Page 2194
... closure in the weak as in the strong operator topology . Thus the strong and weak operator closures of an algebra of ... closure of the algebra generated by the projections in its resolution of the identity , the problem of the present ...
... closure in the weak as in the strong operator topology . Thus the strong and weak operator closures of an algebra of ... closure of the algebra generated by the projections in its resolution of the identity , the problem of the present ...
Page 2217
... closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B1 and an x in X such that ...
... closure . By Lemma 3 , B is bounded and thus B1 is also a bounded Boolean algebra of projections in X. Suppose that B1 is not complete . By Lemma 4 there is a monotone increasing generalized sequence { E } in B1 and an x in X such that ...
Page 2286
... closure Q of AQA - 1 is a bounded normal operator . For each bounded Borel function g on the plane let ( g ) denote the closure of AS ( g ) A - 1 . The correspondence т : S ( g ) → Š ( g ) preserves the operational calculus and ĕ ...
... closure Q of AQA - 1 is a bounded normal operator . For each bounded Borel function g on the plane let ( g ) denote the closure of AS ( g ) A - 1 . The correspondence т : S ( g ) → Š ( g ) preserves the operational calculus and ĕ ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
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