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 86
Page 2154
... dense in . By induction , it is seen that the manifold ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } - is dense in for all k≥ 0. This fact will be stated in the following lemma for future reference . 6 LEMMA . A complex number is ...
... dense in . By induction , it is seen that the manifold ( T − XI ) n + kX + { x | ( T — λI ) n + kx = 0 } - is dense in for all k≥ 0. This fact will be stated in the following lemma for future reference . 6 LEMMA . A complex number is ...
Page 2156
... dense in X. Since M2 is dense in X , the manifold ( \ 1I − T ) TM M2 + { x | ( λ1I − T ) x = 0 } is dense in X , so that ( λ1I — T ) Ŋ ( λ2 I — T ) 1X + { x | ( λ1I − T ) ̃x = 0 } + { x | ( ^ 2I − T ) x = 0 } — is also dense in X ...
... dense in X. Since M2 is dense in X , the manifold ( \ 1I − T ) TM M2 + { x | ( λ1I − T ) x = 0 } is dense in X , so that ( λ1I — T ) Ŋ ( λ2 I — T ) 1X + { x | ( λ1I − T ) ̃x = 0 } + { x | ( ^ 2I − T ) x = 0 } — is also dense in X ...
Page 2159
... dense on T 。. Some results in this direction will be found in the next four lemmas . 11 LEMMA ( G ) . The union of all intervals of constancy relative to T is an open set dense in г. PROOF . It is clear that the union of intervals of ...
... dense on T 。. Some results in this direction will be found in the next four lemmas . 11 LEMMA ( G ) . The union of all intervals of constancy relative to T is an open set dense in г. PROOF . It is clear that the union of intervals of ...
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