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 67
Page 1936
... restriction T | EX is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( o ; T ) in the resolution of the identity for T ...
... restriction T | EX is the corresponding restriction of the resolution of the identity for T. PROOF . Let T be a spectral operator . By Corollary 7 , E , commutes with every projection E ( o ; T ) in the resolution of the identity for T ...
Page 2094
... restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of X ...
... restriction T of T to Y is spectral . The situation corresponding to an invariant closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an invariant closed subspace of X ...
Page 2228
... restriction T | E ( 0 ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , T | E ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
... restriction T | E ( 0 ) X of T to E ( o ) X is a spectral operator whose resolution of the identity is the restriction of E to E ( o ) X . If o is bounded , T | E ( o ) X is bounded . PROOF . If σ is bounded , then by Definition 1 ( i ) ...
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