## Linear Operators: General theory |

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Page 478

The adjoint T * of a linear operator T in B ( X , Y ) is the

The adjoint T * of a linear operator T in B ( X , Y ) is the

**mapping**from Y * to X * defined by T * y * = y * T . 2 LEMMA . The**mapping**T → T * is an isometric isomorphism of B ( X , Y ) into B ( Y * , X * ) . PROOF .Page 493

Conversely , if ( a ) and ( b ) are satisfied for the

Conversely , if ( a ) and ( b ) are satisfied for the

**mapping**which sends æ * into u ( • ) ** , then it follows that for each fixed fe C ( S ) the**mapping**s ) is continuous in the X topology of X * and therefore ( V.3.9 ) is generated ...Page 525

valued u - measurable functions defined on S. Let T be a linear

valued u - measurable functions defined on S. Let T be a linear

**mapping**of X into M. If T is a bounded linear**mapping**of X into L ( S , E , u ) , let Tl , be the norm of this operator , otherwise let Tl , +00 .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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