## Linear Operators: General theory |

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Page 239

It consists of ordered n - tuples x = : [ Q2 , ... , com ] On and has the

It consists of ordered n - tuples x = : [ Q2 , ... , com ] On and has the

**norm**of scalars 1 n lcc - Σ { 10 ; \ } 1 / p . l « 3. The space 1 ' " is the linear space of all ordered n - tuples [ 01 , an ] of scalars ( 2 , ... , Chon with ...Page 240

The space bs is the linear space of all sequences x = { an } of scalars for which the

The space bs is the linear space of all sequences x = { an } of scalars for which the

**norm**n | oc | sup Σα , 72 is finite . 11. The space cs is the linear space of all sequences x = { an } for which the series 2n 1 On is convergent .Page 532

21 Show that the map T defined by ( a ) ( Hardy ) ( THY ) = } [ " Pludy ( T } ) ( ) = S. dy is a map in L ( 0,00 ) of

21 Show that the map T defined by ( a ) ( Hardy ) ( THY ) = } [ " Pludy ( T } ) ( ) = S. dy is a map in L ( 0,00 ) of

**norm**p / ( p - 1 ) , p > 1 , ( b ) ( Hilbert , Schur , Hardy , M. Riesz ) f ( y ) Jo + y is a map in L , ( 0 , ) of ...### 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