## Linear Operators: General theory |

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Page 458

5 If the closed unit

5 If the closed unit

**sphere**of an infinite dimensional B - space X contains only a 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 ...Page 470

... to Rothe [ 1 ] : A continuous mapping of the solid unit

... to Rothe [ 1 ] : A continuous mapping of the solid unit

**sphere**S of a B - space X into a conditionally compact subset of X , which sends the boundary { x \ | a1 = 1 } into S , has at least one fixed point .Page 485

Since the closed unit

Since the closed unit

**sphere**$ * of Y * is Y - compact ( V.4.2 ) , it follows from Lemma 7 and Lemma 1.5.7 that T * S ... If S , S ** are the closed unit**spheres**in X , X ** , respectively , and if x is the natural embedding of X into X ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero