## 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 onto the closed subspace of Lo consisting of those F all of whose negative Fourier coefficients vanish . 55 Using the notations of**Exercises**53 and 54 ...Page 371

( Hint : Generalize the argument of

( Hint : Generalize the argument of

**Exercise**85 to apply to zeros on the boundary of the unit disc . ) 88 Show that**Exercise**87 is valid even if p = 1 . 89 Every function f in H , can be written as a product gh , where y and h are 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 simple theme given in**Exercise**15 , which lends itself to surprisingly manifold ...### 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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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions 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 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