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
... measure space of projec- tions in S. Associated with the spectral measure space ( S , E , e ) is the B * -algebra eB ( S , E ) of e - essentially bounded E - measurable complex valued functions á on S. The norm in eB ( , ) is its e ...
... measure space of projec- tions in S. Associated with the spectral measure space ( S , E , e ) is the B * -algebra eB ( S , E ) of e - essentially bounded E - measurable complex valued functions á on S. The norm in eB ( , ) is its e ...
Page 1983
... space . Suppose that , for each s in S , there are p distinct eigenvalues ... measure . The operators in the non - commutative B * -algebra Ao are then ... space of the preceding section as the one point compactification of RN by the ...
... space . Suppose that , for each s in S , there are p distinct eigenvalues ... measure . The operators in the non - commutative B * -algebra Ao are then ... space of the preceding section as the one point compactification of RN by the ...
Page 2110
... measure into the space of con- μ tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
... measure into the space of con- μ tinuous operators in a space E in which closed bounded sets are compact ( for example , a Montel space ) , then μ is purely atomic . In Walsh [ 3 ] this was extended to the case where E has the property ...
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