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 56
Page 1951
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 σ belongs to J. If 3 is closed , then S and N also belong to J. PROOF . Let 0 ō and let T , = TE ( o ) | E ( o ) X , the restriction of T to the ...
... belong to the right ( left ) ideal J in B ( X ) . Then every projection E ( o ) with 0 σ belongs to J. If 3 is closed , then S and N also belong to J. PROOF . Let 0 ō and let T , = TE ( o ) | E ( o ) X , the restriction of T to the ...
Page 2264
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
... belongs to the point ( respectively residual or continuous ) spectrum of S if and only if it belongs to the point ( respectively residual or continuous ) spectrum of S2 . Since S2 is a spectral operator of scalar type , we have ( S2 — v ...
Page 2462
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( T , A ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
... belongs to the trace class . Then , by what we have already proved , T , A converges to zero in norm , and thus , by Lemma XI.9.9 , TC = ( T , A ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
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