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This text is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. It aims at providing some insight into basic abstract analysis which is now the contextual language of much modern mathematics. Although it is assumed that the student will have familiarity with elementary real and complex analysis and linear algebra and have studied a course in the analysis of metric spaces, a knowledge of integration theory or general topology is not required. The theme of this text concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. But the implications of the general theory are illustrated with a great variety of example spaces.

Normed linear spaces. --- Mathematical analysis.

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Interpolation spaces --- Normed linear spaces --- Scattering (Mathematics)

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Functional analysis --- Normed linear spaces. --- Mathematical analysis. --- Normed linear spaces --- Mathematical analysis

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Differentiable mappings. --- Applications différentiables. --- Espaces linéaires normés. --- Normed linear spaces

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This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-d

Normed linear spaces. --- Linear normed spaces --- Normed vector spaces --- Banach spaces --- Functional analysis --- Vector analysis