## Linear Operators: General theory |

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Page 365

Show that the map : f + f defined in

Show that the map : f + f defined in

**Exercise**53 maps H , in a linear one - one manner ... 55 Using the notations of**Exercises**53 and 54 , show that if fe H ...Page 371

86 Let p , f be as in

86 Let p , f be as in

**Exercise**85. Then ( et ) 0 for almost all 0 . 87 Let p > 1 and let f be a function in Hp . Then there exists a function g in H ...Page 531

This is the vector form of

This is the vector form of

**Exercise**6. ) C. Inequalities of Hardy - Hilbert type . The next set of inequalities are all variations on the surprisingly ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

81 other sections not shown

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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