## Linear Operators: General theory |

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Page 36

This independence is readily proved if there is a finite Hamel

This independence is readily proved if there is a finite Hamel

**basis**, in which case the space is said to be finite dimensional . In a finite dimensional space , a Hamel**basis**is usually called a**basis**. A function T is said to be a ...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 x € X there corresponds a unique sequence { 0 ; } of scalars such that n lim la – E aşxil = 0 . Let { wn } be a**basis**in the F - space X , and let y be the vector ...Page 254

Thus by forming the chain UB , Uq , ... , Ug's 0 g , it is seen that vp is equivalent to vge and thus that vp is in V. Since { vp } is a

Thus by forming the chain UB , Uq , ... , Ug's 0 g , it is seen that vp is equivalent to vge and thus that vp is in V. Since { vp } is a

**basis**, the vector u , has an expansion of the form u = Ep ( uz , vplup , so that u , is in the ...### 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