## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 21

Page 2460

is a

17 ) ( Fil - A ) { ( Fil – H ) - ° / Lac ( H ) } = 1 , it follows from Corollary XII . 4 . 13 ( b

) that À is self adjoint . We may show similarly that H | ( sing ( H ) n D ( H ) ) is a ...

is a

**symmetric operator**in Lac ( H ) , and it follows easily that it is closed . Since (17 ) ( Fil - A ) { ( Fil – H ) - ° / Lac ( H ) } = 1 , it follows from Corollary XII . 4 . 13 ( b

) that À is self adjoint . We may show similarly that H | ( sing ( H ) n D ( H ) ) is a ...

Page 2466

Let ro denote the set of all

– H ) - 1 is compact , and such that the operator ( il – H ) - 1 V E ( e ) belongs to

the trace class whenever e is a finite subinterval of R . We introduce a norm into V

...

Let ro denote the set of all

**symmetric operators**V in H ' such that the operator Vil– H ) - 1 is compact , and such that the operator ( il – H ) - 1 V E ( e ) belongs to

the trace class whenever e is a finite subinterval of R . We introduce a norm into V

...

Page 2478

Suppose that Ve is a

operator V ( il – H2 ) - 1 is com pact , and that for each bounded interval e of the

real axis the operator ( il – H2 ) - 1V4E4 ( e ) is of trace class . Then ( a ) H = H4 +

...

Suppose that Ve is a

**symmetric operator**in H , that D ( V4 ) 2 D ( Hą ) , that theoperator V ( il – H2 ) - 1 is com pact , and that for each bounded interval e of the

real axis the operator ( il – H2 ) - 1V4E4 ( e ) is of trace class . Then ( a ) H = H4 +

...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

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