## Linear Operators: General theory |

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Page 120

If we put t alla b - 1 / P we obtain the

If we put t alla b - 1 / P we obtain the

**inequality**ab app +69/9 , valid for a , b > 0 ; hence , the**inequality**| ab | = | a | p / p + 16 ° / q is valid for all scalars a , b . Putting a = f ( s ) / \ | lp , b = g ( s ) // g | q ...Page 121

Thus where no confusion will result , we shall speak simply of “ a function in Ly ” . In the sequel the symbol | rather than [ 1 ] will be used for an element in Lp . We observe that the

Thus where no confusion will result , we shall speak simply of “ a function in Ly ” . In the sequel the symbol | rather than [ 1 ] will be used for an element in Lp . We observe that the

**inequality**of Minkowski and in ...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 either x or Y is zero . Hence suppose that x + 0 + y . For an arbitrary complex ...### 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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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero