## Linear Operators: General theory |

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Page 239

It consists of ordered n - tuples x = [ ( y , ... , km ] of scalars de . , Ohn and has the

tuples [ ( y , ... , an ] of scalars Oy , ... , Olon with the

It consists of ordered n - tuples x = [ ( y , ... , km ] of scalars de . , Ohn and has the

**norm**2 ( x ) = { 10 " } 1 / . 3. The space 1'e is the linear space of all ordered n -tuples [ ( y , ... , an ] of scalars Oy , ... , Olon with the

**norm**| x1 = sup loilo 1Sisn 4.Page 472

168 ] showed that the

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 ) , that the

168 ] showed that the

**norm**in C [ 0 , 1 ] is strongly differentiable at X , e 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 ) , that the

**norm**in Lp ...Page 532

21 Show that the map T defined by ( a ) ( Hardy ) ( Tf ) ( x ) Г. Кузду is a map in L ,

( 0,00 ) of

Tf ) ( x ) = ( TF ) x ) = $ at dy 00 ES is a map in L , ( 0 , ) of

21 Show that the map T defined by ( a ) ( Hardy ) ( Tf ) ( x ) Г. Кузду is a map in L ,

( 0,00 ) of

**norm**p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) f ( y ) (Tf ) ( x ) = ( TF ) x ) = $ at dy 00 ES is a map in L , ( 0 , ) of

**norm**( sin a / p ) -1 , p ...### 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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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