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 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 B12 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 B12 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 σ : S ( g ) → Ŝ ( g ) preserves the operational calculus and where ...
... 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 σ : S ( g ) → Ŝ ( g ) preserves the operational calculus and where ...
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