## Linear Operators: General theory |

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In particular , if A is a sequence { an } then lim sup A and lim inf A are usually denoted by lim sup an , lim inf an ,

In particular , if A is a sequence { an } then lim sup A and lim inf A are usually denoted by lim sup an , lim inf an ,

**respectively**. If a and b are extended real numbers , then the symbol ( a , b ) denotes the open interval defined by ...Page 484

We have already observed ( 2.3 ) that the adjoint T * of any T in B ( X , Y ) is continuous relative to the X , Y topologies in X * , Y * ,

We have already observed ( 2.3 ) that the adjoint T * of any T in B ( X , Y ) is continuous relative to the X , Y topologies in X * , Y * ,

**respectively**. The following result shows that , if T is weakly compact , its adjoint T * has a ...Page 485

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

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

**respectively**. If S , S ** are the closed unit spheres in X , X ** ,**respectively**, and if x ...### 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