## Linear Operators: General theory |

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Page 17

A topological space X is said to be locally

neighborhood whose closure is

intersection property if every finite subfamily has a non - void intersection . A

subset of X is called ...

A topological space X is said to be locally

**compact**if every point has aneighborhood whose closure is

**compact**. A family of sets has the finiteintersection property if every finite subfamily has a non - void intersection . A

subset of X is called ...

Page 483

If T is weakly

) is

If T is weakly

**compact**, then TS is**compact**in the Y * topology of Y and thus x ( TS) is

**compact**and hence closed in the Y * topology of Y ** . Thus if T is weakly**compact**, ( i ) yields T ** ( S ) Cx ( TS ) . According to Theorem V.4.5 , S , = S ** ...Page 494

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally

weakly

By Theorem 4.8 this implies that T is a weakly

From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally

weakly

**compact**set of rca ( S ) , and therefore T * is a weakly**compact**operator .By Theorem 4.8 this implies that T is a weakly

**compact**operator . Q.E.D. given ...### 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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