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Elements of Non-Linear Functional Analysis

Richard A. Graff

出版	American Mathematical Soc., 1978
主題	Mathematics / CalculusMathematics / Functional AnalysisScience / General
ISBN	08218220639780821822067
URL	http://books.google.com.hk/books?id=NBHUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

A new notion of Frechet differentiability is introduced for maps between Banach spaces which are dual spaces, and it is shown that diffeomorphisms in the class of mappings thus isolated preserve the bounded weak-star topology as well as the ordinary metric topology. Basic Banach manifold differential topology is redeveloped under the assumption that the transition functions between the coordinate charts possess this refined type of differentiability, and it is pointed out that such manifolds possess additional structures not found on general manifolds: for example, a globally defined weaker topology, and Finsler metrics in which boundedness is equivalent to compact closure in the global weaker topology.