## 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 ay ) 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 ay ) 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

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