Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 88
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 H " . 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 ) p was differentiable for t > 0 and an arbitrary in H " . 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 Io having positive length and let Yn = { ^ λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4 xo } = = { λ 。| λ ...
... clear that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of Io having positive length and let Yn = { ^ λo | λo € y , | λ — λ 。| " | R ( λ ; T ) | ≤ 1 , do ‡ λ € 4 xo } = = { λ 。| λ ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero