## Linear Operators: General theory |

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Page 121

... rather than classes of equivalent functions . Thus where no confusion will result

, we shall speak simply of “ a function in Lo ” . In the sequel the symbol í rather

than [ 1 ] will be used for an element in Ly . We observe that the

... rather than classes of equivalent functions . Thus where no confusion will result

, we shall speak simply of “ a function in Lo ” . In the sequel the symbol í rather

than [ 1 ] will be used for an element in Ly . We observe that the

**inequality**of ...Page 248

The above

follows from the postulates for ħ that the Schwarz

is zero . Hence suppose that # # 0 #y . For an arbitrary complex number a 0 = ( x

+ ...

The above

**inequality**, known as the Schwarz**inequality**, will be proved first . Itfollows from the postulates for ħ that the Schwarz

**inequality**is valid if either x or yis zero . Hence suppose that # # 0 #y . For an arbitrary complex number a 0 = ( x

+ ...

Page 370

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

ini 79 The

n is odd , the

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

ini 79 The

**inequality**| x ' ( 1 ) S no max ix ( t ) , -1 Sisi holds for each x in Pn . 80 Ifn is odd , the

**inequality**læ ' ( 0 ) En max | æ ( t ) | -1 SiS + 1 holds for each x in ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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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