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 1964
... space of projec- tions in S. Associated with the spectral measure space ( S , E , e ) is the B * -algebra eB ( S , E ) ... topological space , we shall assume that contains the Borel subsets of S and that e ( 0 ) 0 if σ is a non - void set ...
... space of projec- tions in S. Associated with the spectral measure space ( S , E , e ) is the B * -algebra eB ( S , E ) ... topological space , we shall assume that contains the Borel subsets of S and that e ( 0 ) 0 if σ is a non - void set ...
Page 2130
... topological space which is also ordered is said to be an ordered topological vector space in case its positive cone is closed . For an exposition of ordered topological vector spaces , we refer the reader to the books of Day [ 12 ] ...
... topological space which is also ordered is said to be an ordered topological vector space in case its positive cone is closed . For an exposition of ordered topological vector spaces , we refer the reader to the books of Day [ 12 ] ...
Page 2187
... space of all E - essentially bounded 2 - measurable functions on A is a B - algebra under the natural operations ( i ) ... topological space and if Σ is the field of Borel sets in 4 , then the symbol EB ( A ) will sometimes be used instead ...
... space of all E - essentially bounded 2 - measurable functions on A is a B - algebra under the natural operations ( i ) ... topological space and if Σ is the field of Borel sets in 4 , then the symbol EB ( A ) will sometimes be used instead ...
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