## Linear Operators: Spectral operators |

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Page 2450

Let A be the set of all

RA belongs to the

the norm of an element A € A is simply the

RA ...

Let A be the set of all

**operators**A e B ( X ) for which AX Ç D ( R ) and for whichRA belongs to the

**HilbertSchmidt**class HS , and let | | | A | | | = | | RA | | , so thatthe norm of an element A € A is simply the

**Hilbert**-**Schmidt**norm of the**operator**RA ...

Page 2493

Then , for sel sufficiently small , Te is similar to the self adjoint operator To ; that is

, there exists an ( analytically varying ) ... If we let sla ) = det ( I – BR ( A ) A ) be

the Hilbert - Fredholm determinant of the

...

Then , for sel sufficiently small , Te is similar to the self adjoint operator To ; that is

, there exists an ( analytically varying ) ... If we let sla ) = det ( I – BR ( A ) A ) be

the Hilbert - Fredholm determinant of the

**Hilbert**-**Schmidt operator**1 – BR ( 2 ) A...

Page 2524

Dockard , D . , and Pearcy , C . 1 . On unitary equivalence of

operators and operators without logarithms . Acta Sci . Math . Szeged 28 , 1 - 7 (

1967 ) .

Dockard , D . , and Pearcy , C . 1 . On unitary equivalence of

**Hilbert**-**Schmidt****operators**. Proc . Amer . Math . Soc . 16 , 671 - 675 ( 1965 ) . 2 . On rootlessoperators and operators without logarithms . Acta Sci . Math . Szeged 28 , 1 - 7 (

1967 ) .

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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