## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

### From inside the book

Results 1-3 of 80

Page 2013

For a sequence { om } satisfying ( 3 ) , A is

consists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

For a sequence { om } satisfying ( 3 ) , A is

**given**by ( 9 ) and the domain of Aconsists precisely of those o for which the limit in ( 9 ) exists . Our next concern

will be with the question of the existence of a resolution of the identity for A . This

leads ...

Page 2088

... complex measurable functions on RN and let As be the densely defined closed

operator

operator whose spectrum lies in a left half plane then it is the infinitesimal

generator ...

... complex measurable functions on RN and let As be the densely defined closed

operator

**given**by equations 12 . 4 . Show that if As is a scalar type spectraloperator whose spectrum lies in a left half plane then it is the infinitesimal

generator ...

Page 2096

Another characterization of subscalar operators is

which asserts that , under certain ... X 2 X which has a continuous projection onto

X . A second proof of this latter result is

Another characterization of subscalar operators is

**given**, based on a theoremwhich asserts that , under certain ... X 2 X which has a continuous projection onto

X . A second proof of this latter result is

**given**in Ionescu Tulcea and Plafker [ 1 ] .### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero