Excellent treatment of subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. Includes detailed proofs of theorems, bibliography, and index of symbols. 1966 edition.
The second edition offers an in-depth analysis of the Hahn-Banach theorem, enriched with concrete examples and historical context. It delves into the theorem's relationship with the axiom of choice and examines the uniqueness of Hahn-Banach extensions. A notable addition is a new chapter dedicated to vector-valued Hahn-Banach extensions, enhancing the book's comprehensiveness and relevance for readers seeking a thorough understanding of this mathematical concept.