## Linear Operators: Spectral operators |

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Page 1994

Let an o

Theorem II . ... Then , by Theorem 4 , ang = F - Xn X , and since ano

we see from the continuity of F that lim s lán ( s ) – 1 ( ) | 2 ds = 0 , m . n + 000

which ...

Let an o

**converge**for each o in H . Theorem 4 shows that lan = panloo , andTheorem II . ... Then , by Theorem 4 , ang = F - Xn X , and since ano

**converges**,we see from the continuity of F that lim s lán ( s ) – 1 ( ) | 2 ds = 0 , m . n + 000

which ...

Page 2218

It must be shown that { Ex }

so a consideration of the sequence { Ea – E } shows that it may be assumed that

E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ex } is ...

It must be shown that { Ex }

**converges**strongly to E . By Lemma 6 , E is in B andso a consideration of the sequence { Ea – E } shows that it may be assumed that

E = 0 . Thus , to make an indirect proof , it is assumed that the sequence { Ex } is ...

Page 2462

Moreover , if C belongs to the trace class C1 , then TnC

trace norm , and CT *

XE H | | x 3 1 } ) is conditionally compact , and thus for each a > 0 there exists a

finite ...

Moreover , if C belongs to the trace class C1 , then TnC

**converges**to zero intrace norm , and CT *

**converges**to zero in trace norm . PROOF . The set K = C ( {XE H | | x 3 1 } ) is conditionally compact , and thus for each a > 0 there exists a

finite ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero