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 |
From inside the book
Results 1-3 of 85
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 ) was differentiable for t > 0 and an arbitrary o in 5o . It is even clear that the nth order derivative T ) ( 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 ) was differentiable for t > 0 and an arbitrary o in 5o . It is even clear that the nth order derivative T ) ( 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 0 Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4 xo = 110 } = { λ ...
... 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 0 Yn = { λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4 xo = 110 } = { λ ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero