## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 36

Page 479

A linear

and only if its

When these inverses exist , ( T - 1 ) * = ( T * ) - 1 . PROOF . If T - 1 exists and is in

B ...

A linear

**operator**T in B ( X , Y ) has a bounded inverse T - 1 defined on all of Y ifand only if its

**adjoint**T * has a bounded inverse ( T * ) - 1 defined on all of X * .When these inverses exist , ( T - 1 ) * = ( T * ) - 1 . PROOF . If T - 1 exists and is in

B ...

Page 538

Notes and Remarks Topologies ,

employed systematically by von Neumann [ 2 ] . The notions of strong and weak ...

Notes and Remarks Topologies ,

**adjoints**and projections . The strong and weak**operator**topologies for bounded operators on Hilbert space were introduced andemployed systematically by von Neumann [ 2 ] . The notions of strong and weak ...

Page 794

Self -

Akad . Nauk SSSR 4 , 53 – 104 ( 1940 ) . ( Russian . English summary ) Math .

Rev . 2 , 104 ( 1941 ) . 8 . Spectral functions of a symmetric

Akad .

Self -

**adjoint**extensions of the second kind of a symmetric**operator**. IzvestiyaAkad . Nauk SSSR 4 , 53 – 104 ( 1940 ) . ( Russian . English summary ) Math .

Rev . 2 , 104 ( 1941 ) . 8 . Spectral functions of a symmetric

**operator**. IzvestiyaAkad .

### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

25 other sections not shown

### Other editions - View all

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm obtained operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero