## Linear Operators: General theory |

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It consists of ordered n - tuples x = [ Q2 , ... , Com ] of scalars Qj , ... , On and has the

It consists of ordered n - tuples x = [ Q2 , ... , Com ] of scalars Qj , ... , On and has the

**norm**n lac ] = { Elain } 110 . { Σ | α . 3. The space Inc is the linear space of all ordered n - tuples [ cy , . .. , Cen ] of scalars Oy ...Page 472

168 ] showed that the

168 ] showed that the

**norm**in C [ 0 , 1 ] is strongly differentiable at x , € C [ 0 , 1 ] if and only if the function X , achieves its maximum at exactly one point . Mazur ( 1 ; p . 78–79 ] proved that the same condition holds in B ( S ) ...Page 532

21 Show that the map T defined by 1 ( a ) ( Hardy ) ( Tf ) ( x ) = - Styldy dy is a map in Ly ( 0 , 0 ) of

21 Show that the map T defined by 1 ( a ) ( Hardy ) ( Tf ) ( x ) = - Styldy dy is a map in Ly ( 0 , 0 ) of

**norm**p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) fly ) ( 7 0 x + y is a map in L , ( 0 , 0 ) of**norm**r ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains 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 Hilbert space 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