Linear Operators: Spectral operators |
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Page 1951
... belong to the right ( left ) ideal 3 in B ( x ) . Then every projection E ( o ) with 0 ‡ ō belongs to J. If I is closed , then S and N also belong to J. ₫ ō PROOF . Let 0 σ and let T , = TE ( o ) | E ( o ) X , the restriction of T to ...
... belong to the right ( left ) ideal 3 in B ( x ) . Then every projection E ( o ) with 0 ‡ ō belongs to J. If I is closed , then S and N also belong to J. ₫ ō PROOF . Let 0 σ and let T , = TE ( o ) | E ( o ) X , the restriction of T to ...
Page 2263
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. - PROOF . It follows from Lemma 19 ...
... belongs to the continuous spectrum of the spectral operator S. The point vo belongs to the point or to the continuous spectrum of the operator S depending on whether vo is or is not an eigenvalue of S. - PROOF . It follows from Lemma 19 ...
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 = ( TA ) 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 = ( TA ) B converges to zero in trace norm . By Lemma XI.9.6 ( c ) and Definition XI.9.1 , C * belongs ...
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