## Linear Operators: General theory |

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Page 245

Every linear operator on a

Every linear operator on a

**finite**dimensional normed linear space is continuous . PROOF . Let { b1 , ... , bn } be a Hamel basis for the**finite**dimensional normed linear space X so that every x in X has a unique representation in the ...Page 290

Now suppose that ( S , , u ) is o -

Now suppose that ( S , , u ) is o -

**finite**, and let En be an increasing sequence of measurable sets of**finite**measure whose union is S. Using the theorem for L ( En ) = L ( En , E ( En ) , m ) , we obtain a sequence { gn } of functions ...Page 849

( See Decomposition ) definition , III.4.3 ( 126 )

( See Decomposition ) definition , III.4.3 ( 126 )

**finite**, III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) a metric space , I11.7.1 ( 158 ) , as measure in a group , ( 90–91 ) topology in. ית ' VIII.6.7 ( 676 ) k - parameter ...### 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 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 Hilbert space 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