Linear Operators: Spectral operators |
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Page 1994
... converges , we see from the continuity of F that An❤ lim | Ã , ( 8 ) — Xm ( 8 ) | 2 ds = 0 , m.n∞ σ An which implies ( III.3.6 ) that I converges in measure on σ . Conversely , if ( 29 ) and ( 30 ) hold , then , since the norms ...
... converges , we see from the continuity of F that An❤ lim | Ã , ( 8 ) — Xm ( 8 ) | 2 ds = 0 , m.n∞ σ An which implies ( III.3.6 ) that I converges in measure on σ . Conversely , if ( 29 ) and ( 30 ) hold , then , since the norms ...
Page 2218
... converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra B is complete . Let { E } be a weakly convergent generalized sequence in B ...
... converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra B is complete . Let { E } be a weakly convergent generalized sequence in B ...
Page 2462
... converges uniformly to zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x ...
... converges uniformly to zero and { CT } converges uniformly to zero . Moreover , if C belongs to the trace class C1 , then TC converges to zero in trace norm , and CT converges to zero in trace norm . - ... " PROOF . The set K = C ( { x ...
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