## Linear Operators: General theory |

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Page 494

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

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**. ByTheorem 4.8 this implies that T is a weakly

**compact operator**. Q.E.D. 4 Theorem.Page 540

operator and the operator mapping into a weakly complete space X. Weakly

discussion of weakly

Grothendieck ...

operator and the operator mapping into a weakly complete space X. Weakly

**compact operators**from C[0, 1] to X were treated by Sirvint [8]. A very incisivediscussion of weakly

**compact operators**with domain C(S) was given byGrothendieck ...

Page 541

compact and

treated the same case for an arbitrary a-finite measure space X obtaining a

representation of the general operator as an integral with respect to a

Lipschitzean ...

compact and

**compact operators**from 1^(5) to an arbitrary space X. Phillips [3]treated the same case for an arbitrary a-finite measure space X obtaining a

representation of the general operator as an integral with respect to a

Lipschitzean ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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