Titlebook: Geometric Functional Analysis and its Applications; Richard B. Holmes Textbook 1975 Springer Science+Business Media New York 1975 Banach S

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Convexity in Linear Topological Spaces,ful methods based on topological concepts. Thus, as our next step, we consider the result of imposing on a given linear space a “compatible topology”. This is hardly a novel idea; indeed, several excellent books already exist which are devoted to a detailed investigation of the many ramifications of

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Principles of Banach Spaces, mappings, extreme points, etc. and the topological notions of openness, compactness, continuity, etc. For such a study the correct setting is, as we have seen, the linear topological space (frequently required also to be locally convex). The resulting theory is broad and powerful, as we hope has be

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Conjugate Spaces and Universal Spaces,ns for optimization theory as we shall see. We shall also establish an isomorphism between certain spaces of Lipschitz functions and certain spaces of L. type. A particular consequence of this is an example of a pair of Banach spaces (namely, .(?.) and .([0, 1])) which fail to be isomorphic, yet whose conjugate spaces are isomorphic.

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Textbook 1975 These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major the

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,über das Dirichletsche Prinzip,rounded duality theory and it is interesting to discover that the maximal class of linear topologies which yields the requisite duality theory is precisely the class of topologies defined by a family of semi-norms.

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Convexity in Linear Topological Spaces,rounded duality theory and it is interesting to discover that the maximal class of linear topologies which yields the requisite duality theory is precisely the class of topologies defined by a family of semi-norms.