## Linear Operators: General theory |

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Page 121

This observation is obvious in the case of Minkowski's

This observation is obvious in the case of Minkowski's

**inequality**. To see that it is justified in case of Hölder's**inequality**, note that Hölder's ...Page 248

The above

The above

**inequality**, known as the Schwarz**inequality**, will be proved first . It follows from the postulates for H that the Schwarz**inequality**is valid if ...Page 370

and the equality is attained only by scalar multiples of the Tchebicheff polynomial in 79 The

and the equality is attained only by scalar multiples of the Tchebicheff polynomial in 79 The

**inequality**lx ' ( 1 ) 5 no max | æ ( t ) | -1 Sisi holds for ...### 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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### Common terms and phrases

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