## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 1094

Statement (a) is evident from Definition 1. To prove (b), we put T = Ti-HT, and

note that, by Corollary 3, Manil (T1-HT2) is unti(T1)+/1.11(T2) Alan 2(Ti-HT2) is u,

11(T1)+/1,12(T2). First let p > 1. Then by Minkowski's

3.

Statement (a) is evident from Definition 1. To prove (b), we put T = Ti-HT, and

note that, by Corollary 3, Manil (T1-HT2) is unti(T1)+/1.11(T2) Alan 2(Ti-HT2) is u,

11(T1)+/1,12(T2). First let p > 1. Then by Minkowski's

**inequality**, oo 1/p co 1/p co (3.

Page 1105

By the continuity of tr(T) for Te C1, the continuity of the product TS which was

noted in the paragraph following Lemma 9, the continuity of the norm function

which follows from the triangle

follows ...

By the continuity of tr(T) for Te C1, the continuity of the product TS which was

noted in the paragraph following Lemma 9, the continuity of the norm function

which follows from the triangle

**inequality**of Lemma 14(d), and by Lemma 11, itfollows ...

Page 1774

A Hilbert space $) is a complea B-space and |(a, y) = |a||y|, a, ye Ş. PRoof. The

above

from the postulates for $5 that the Schwarz

zero.

A Hilbert space $) is a complea B-space and |(a, y) = |a||y|, a, ye Ş. PRoof. The

above

**inequality**, known as the Schwarz**inequality**, will be proved first. It followsfrom the postulates for $5 that the Schwarz

**inequality**is valid if either a or y iszero.

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero