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 1931
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
... clear to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to any such spectral ...
Page 2053
... clear from the form of exp t that T ( t ) p was differentiable for t > 0 and an arbitrary in HP . It is even clear that the nth order derivative Tn ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
... clear from the form of exp t that T ( t ) p was differentiable for t > 0 and an arbitrary in HP . It is even clear that the nth order derivative Tn ( t ) exists in the uniform operator topology for t > 0 and every positive integer n ...
Page 2159
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of To having positive length and let Yn = { λo | do € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4x0 } = { λ 。| λo € y ...
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of To having positive length and let Yn = { λo | do € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4x0 } = { λ 。| λo € y ...
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