## Linear Operators, Part 1 |

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Page 458

If the closed unit

finite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

If the closed unit

**sphere**of an infinite dimensional B - space X contains only afinite number of extremal points , then X is not isometrically isomorphic to the

conjugate of any B - space . 6 Let S be a topological space , and let C ( S ) be the

B ...

Page 470

... generalizations of fixed point theorems , we mention the following due to Rothe

[ 1 ] : A continuous mapping of the solid unit

conditionally compact subset of X , which sends the boundary { x || w | = 1 } into S

...

... generalizations of fixed point theorems , we mention the following due to Rothe

[ 1 ] : A continuous mapping of the solid unit

**sphere**S of a B - space X into aconditionally compact subset of X , which sends the boundary { x || w | = 1 } into S

...

Page 485

Since the closed unit

Lemma 7 and Lemma 1.5.7 that T * S * is ... If S , S ** are the closed unit

in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by ...

Since the closed unit

**sphere**S * of Y * is y - compact ( V.4.2 ) , it follows fromLemma 7 and Lemma 1.5.7 that T * S * is ... If S , S ** are the closed unit

**spheres**in X , X ** , respectively , and if x is the natural embedding of X into X ** , then by ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero