## Linear Operators: General theory |

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Page 121

We observe that the

We observe that the

**inequality**of Minkowski and ( in the case of scalar valued functions ) the**inequality**of Hölder may be regarded as applying to the spaces Ly . This observation is obvious in the case of Minkowski's**inequality**.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 ...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 each x in Pn . 80 If n is odd , the**inequality**læ ' ( 0 ) En max | æ ( t -1 StS + ...### 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