## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 54

Page 2094

The situation corresponding to an

The situation corresponding to an

**invariant**closed subspace of T is not so simple . However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an**invariant**closed subspace y of X is spectral if and only if the ...Page 2214

Then an operator is in the weakly closed algebra generated by B if and only if it leaves

Then an operator is in the weakly closed algebra generated by B if and only if it leaves

**invariant**every closed linear manifold which is**invariant**under every member of B. PROOF . It was observed in the preceding proof that an operator ...Page 2216

To do this , let A be an operator in A , and let H. be a closed subspace of Hilbert space which is

To do this , let A be an operator in A , and let H. be a closed subspace of Hilbert space which is

**invariant**under every element E ( e ) of the resolution of the identity for T. Thus , if P is the orthogonal projection onto Ho then ...### 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 | 1929 |

Copyright | |

32 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit 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