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Linear analysis. An introductory course. (English) Zbl 0753.46002

Cambridge Mathematical Textbooks. Cambridge etc.: Cambridge University Press,. xi, 240 p. (1990).
This book is an introduction to linear functional analysis. The exposition is clear, enthusiastic, precise, with scientific rigor and many exercises. So it may be strongly recommended as a basic textbook.
Together with classical materials such as the Hahn-Banach theorem, Baire theorem, contractions, duality, Hilbert spaces, or algebras of operators; it also includes special topics such as the geometry of finite dimensional spaces and fixed point theorems. On the other hand, notes at the end of the chapters briefly describe the origin and evolution of the subjects from the bibliographic point of view. So the present book may be also recommended to postgraduated students or for consultation.

MSC:

46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
46B07 Local theory of Banach spaces
46B20 Geometry and structure of normed linear spaces
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46B10 Duality and reflexivity in normed linear and Banach spaces
46L05 General theory of \(C^*\)-algebras
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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