## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 89

Page 1928

... how far the theory may be applied to non - symmetric boundary value problems

. 2 . Terminology and Preliminary Notions The concepts of a Boolean algebra of

... how far the theory may be applied to non - symmetric boundary value problems

. 2 . Terminology and Preliminary Notions The concepts of a Boolean algebra of

**projections**, a spectral measure , an integral with respect to a spectral measure ...Page 2218

PROOF . Since a spectral operator of scalar type is clearly in the weakly closed

algebra A generated by the

to show that every operator in A is a spectral operator of scalar type . This follows

...

PROOF . Since a spectral operator of scalar type is clearly in the weakly closed

algebra A generated by the

**projections**in its resolution of the identity , it sufficesto show that every operator in A is a spectral operator of scalar type . This follows

...

Page 2300

P Then , since the collection of finite sums of

bounded , it is clear from [ * ] that the collection of finite sums of

T + P ) , n 2 K , is uniformly bounded . Moreover , L = 8 ( Eldin ; T ) – Elum ; T + P ...

P Then , since the collection of finite sums of

**projections**E ( / n ; T ' ) is uniformlybounded , it is clear from [ * ] that the collection of finite sums of

**projections**Elun ;T + P ) , n 2 K , is uniformly bounded . Moreover , L = 8 ( Eldin ; T ) – Elum ; T + P ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

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