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 2187
... measurable function which coincides with f , E - almost everywhere on Д. It should also be noted that the space of all E - essentially bounded 2 - measurable functions ... measurable func- tions on 4 and a B - algebra of spectral operators ...
... measurable function which coincides with f , E - almost everywhere on Д. It should also be noted that the space of all E - essentially bounded 2 - measurable functions ... measurable func- tions on 4 and a B - algebra of spectral operators ...
Page 2409
... measurable functions defined in D and satisfying ( 7 ) , we may let be an arbitrary complex B - space , and can consider the space L2 ( D , X ) of X - valued Borel - Lebesgue measurable functions defined in D. ( b ) We may replace the ...
... measurable functions defined in D and satisfying ( 7 ) , we may let be an arbitrary complex B - space , and can consider the space L2 ( D , X ) of X - valued Borel - Lebesgue measurable functions defined in D. ( b ) We may replace the ...
Page 2410
... measurable function defined in D × D , with values in the space B ( X ) of ... functions defined in D and satisfying ( 33 ) . Let 1 / pl / p'1 . Let e1 ... functions f such that f ( z ) = X ; for all zee ,, 1 ≤ j < ∞ . Let T be the ...
... measurable function defined in D × D , with values in the space B ( X ) of ... functions defined in D and satisfying ( 33 ) . Let 1 / pl / p'1 . Let e1 ... functions f such that f ( z ) = X ; for all zee ,, 1 ≤ j < ∞ . Let T be the ...
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