## Linear Operators: Spectral operators |

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Page 1994

Let Ano

Theorem II . 3 . ... Then , by Theorem 4 , ang = F - Xn X , and since Ano

, we see from the continuity of F that lim 11 ( 8 ) – Im ( s ) / 2 ds = 0 , m . no which ...

Let Ano

**converge**for each o in H . Theorem 4 shows that 1an1 = panloo , andTheorem II . 3 . ... Then , by Theorem 4 , ang = F - Xn X , and since Ano

**converges**, we see from the continuity of F that lim 11 ( 8 ) – Im ( s ) / 2 ds = 0 , m . no which ...

Page 2218

It must be shown that { Ea }

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 { Ea }

**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 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero