## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 69

Page 2403

We then use this inequality to

We then use this inequality to

**apply**Theorem 1 in an illustrative but somewhat artificial setting , essentially to ... A first**application**( Theorem 6 ) is made in this way , and immediately following upon this we develop a similar but ...Page 2413

Q.E.D. > Theorem 1 and its corollaries are readily generalized to

Q.E.D. > Theorem 1 and its corollaries are readily generalized to

**apply**to unbounded operators . 2 8 THEOREM . Let X be a B - space , and let T be a closed , densely defined operator in X , with domain D ( T ) .Page 2434

**Applying**Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate " diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may**apply**Theorem 21 to analyze a variety of operators .### 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