## Linear Operators: General theory |

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Page 239

Ohn and has the

of all ordered n - tuples x = [ Q , . . . , an ] of scalars az , . . . , Olon with the

= sup laila 1Sisn 4 . The space l , is defined for 1 Sp < oo as the linear space of ...

Ohn and has the

**norm**| x ) = { } | . . / p } 1 / 0 . 3 . The space I " . is the linear spaceof all ordered n - tuples x = [ Q , . . . , an ] of scalars az , . . . , Olon with the

**norm**lx |= sup laila 1Sisn 4 . The space l , is defined for 1 Sp < oo as the linear space of ...

Page 472

168 ] showed that the

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 , € C [ 0 , 1 ] ifand 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 |

Algebraic Preliminaries | 34 |

Copyright | |

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