## Linear Operators: General theory |

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It consists of ordered n - tuples x = [ 0 , ... , O.n ] . . . , Chen and has the

It consists of ordered n - tuples x = [ 0 , ... , O.n ] . . . , Chen and has the

**norm**of scalars c13 n | x ] = { 10 ; \ } l / p . = r --- 3. The space 1 " . is the linear space of all ordered n - tuples ( an , On ] of scalars dj , .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 ) ( T / ) ( x ) = - f ( y ) dy Г. p 00 ES - dy is a map in L , ( 0 , 0 ) of

21 Show that the map T defined by 1 ( a ) ( Hardy ) ( T / ) ( x ) = - f ( y ) dy Г. p 00 ES - dy is a map in L , ( 0 , 0 ) of

**norm**p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) f ( y ) ( T / ) ( x ) o x + y is a ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad 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 semi-group 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