## Linear Operators: General theory |

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Page 479

A linear

and only if its

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

...

Page 538

The strong and weak operator topologies for bounded operators on Hilbert space

were introduced and employed ... The formal concept of the

back to matrix theory and to the theories of differential and integral equations .

The strong and weak operator topologies for bounded operators on Hilbert space

were introduced and employed ... The formal concept of the

**adjoint operator**goesback to matrix theory and to the theories of differential and integral equations .

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 .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero