Linear Operators: Spectral operators |
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Page 2197
... sequence ( a monotone sequence ) in B. Then , if { E } is increasing , lim Ex = α ( V Ea ) x , xЄX , while if { E } is decreasing , then lim Ex = E x Є X. α α α Conversely , if every monotone increasing generalized sequence ( monotone ...
... sequence ( a monotone sequence ) in B. Then , if { E } is increasing , lim Ex = α ( V Ea ) x , xЄX , while if { E } is decreasing , then lim Ex = E x Є X. α α α Conversely , if every monotone increasing generalized sequence ( monotone ...
Page 2218
... sequence in B and suppose that its limit E is a projection . It must be shown that { E } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E - E } shows that it may be assumed that E = 0. Thus , to ...
... sequence in B and suppose that its limit E is a projection . It must be shown that { E } converges strongly to E. By Lemma 6 , E is in B and so a consideration of the sequence { E - E } shows that it may be assumed that E = 0. Thus , to ...
Page 2450
... sequence { n } contains no repetitions ) and that λ # 0 for n ≥ 1. By Corollary X.3.5 we have A. Let r , be the distance from the eigenvalue λ , to the other points on the spectrum of T , so that r2 > 0 , while , of course , the sequence ...
... sequence { n } contains no repetitions ) and that λ # 0 for n ≥ 1. By Corollary X.3.5 we have A. Let r , be the distance from the eigenvalue λ , to the other points on the spectrum of T , so that r2 > 0 , while , of course , the sequence ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero