## Linear Operators: General theory |

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It follows readily from Theorem 2.7 that in every linear vector space X there is a maximal linearly independent set B. A subset B of the linear space X is called a Hamel

It follows readily from Theorem 2.7 that in every linear vector space X there is a maximal linearly independent set B. A subset B of the linear space X is called a Hamel

**basis**or a Hamel base for X if every vector x in X has a unique ...Page 71

A sequence { Xn } in an F - space X is called a

A sequence { Xn } in an F - space X is called a

**basis**for X if to each xe X there corresponds a unique sequence { Q } of scalars such that lim ( 2 – 3 arti ! 0 . n n - 00 8 Let ( wn } be a**basis**in the F - space X , and let y be the ...Page 254

Thus by forming the chain Up , Ug , Uz's V g . it is seen that vg is equivalent to vz , and thus that Vp is in V. Since { vp } is a

Thus by forming the chain Up , Ug , Uz's V g . it is seen that vg is equivalent to vz , and thus that Vp is in V. Since { vp } is a

**basis**, the vector u , has an expansion of the form un = { ( ux , vg ) vg , so that u , is in the closed ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero