## 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 - 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 612

For example , Weyl [ 2 ] showed that if T is a self

have void point spectrum ) on a separable Hilbert space , then a self adjoint

compact operator K may be found such that T + K has enough eigenvectors to

span the ...

For example , Weyl [ 2 ] showed that if T is a self

**adjoint operator**( which mayhave void point spectrum ) on a separable Hilbert space , then a self adjoint

compact operator K may be found such that T + K has enough eigenvectors to

span the ...

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 |

quences | 26 |

Copyright | |

80 other sections not shown

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