## Linear Operators: General theory |

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Page 421

**Hence**mg ( ro ) g ( mxo ) / < 1 , from which we conclude that g ( ro ) = 0. That is , g ( x ) = 0 ) , whenever fi ( x ) ) = 0 for i = 1 , ... , n .Page 423

**Hence**\ y * ( Tx ) ) < € , so that Tx € N ( 0 ; y * , ... Y * , £ ) . Therefore , T'is weakly continuous at the origin , and**hence**at every point .Page 485

**Hence**T * is weakly compact . Conversely , if T * is weakly compact , it follows from Lemma 7 that T ** is continuous relative to the X * , Y *** topologies ...### 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