## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 97

Page 1951

By

By

**Corollary**V1.5.5 the compact operators form a closed twosided ideal in B ( X ) and so the present**corollary**is immediate . Q.E.D. 4**COROLLARY**. If T is weakly compact , then so are S , N , and every projection E ( o ) with 0 € 0 .Page 1952

0 0 6

0 0 6

**COROLLARY**. If A , T = 0 ( respectively TA , = 0 ) , then A , S = A , N = A , E ( 0 ) = 0 if 0 0 0 ( respectively SA , = NA . = E ( 0 ) A , = 0 if 0 € 7 ) . 7**COROLLARY**. A spectral operator is of finite type if and only if it is ...Page 2192

This shows that o ( S ( f ) ) = f ( 0 ) 2 0 $ ( 8 ) E ( O ) = 1 a and completes the proof of the lemma , Q.E.D. 12

This shows that o ( S ( f ) ) = f ( 0 ) 2 0 $ ( 8 ) E ( O ) = 1 a and completes the proof of the lemma , Q.E.D. 12

**COROLLARY**. Let A be an algebra of operators in a weakly complete B - space X. Suppose that A is topologically and ...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1931 |

Copyright | |

30 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero