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 83
Page 1951
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF ...
... Corollary VI.5.5 the compact operators form a closed two- sided ideal in B ( X ) and so the present corollary is immediate . Q.E.D. 4 COROLLARY . If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 ō . PROOF ...
Page 1952
... Corollary 6 that NP + 1 0 and so T is of finite type . Q.E.D. 8 COROLLARY . If Tx = 0 , then Sx - Nx = E ( o ) x = 0 if 0 ‡ ō . PROOF . For a given x in X , the class of bounded linear operators in X for which Ax = 0 is a closed left ...
... Corollary 6 that NP + 1 0 and so T is of finite type . Q.E.D. 8 COROLLARY . If Tx = 0 , then Sx - Nx = E ( o ) x = 0 if 0 ‡ ō . PROOF . For a given x in X , the class of bounded linear operators in X for which Ax = 0 is a closed left ...
Page 2192
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
... COROLLARY . Every operator in the uniformly closed algebra genera- ted by a bounded Boolean algebra of projection operators in a weakly complete B - space is a scalar type spectral operator . PROOF . This follows from Corollary 12 and ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
20 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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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