The reviewer appreciates the concise yet comprehensive coverage of functional analysis in Barbara MacCluer's book, noting its suitability for beginners in graduate studies. They highlight the inclusion of complex analysis and operator theory, though they question the necessity of concrete Hilbert space examples.
The reviewer finds Barbara MacCluer's 'Elementary Functional Analysis' to be a valuable addition to the field, particularly for its concise yet thorough treatment of the subject. Aimed at beginning graduate students, the book requires minimal prerequisites and covers essential topics in Banach and Hilbert space theory, operator theory, and foundational results like the Hahn-Banach theorem. The reviewer appreciates the inclusion of complex analysis and the wealth of examples provided, which help illustrate abstract concepts. However, they question the necessity of concrete Hilbert space examples, given the abstract nature of the subject. Overall, the book is seen as a potential canonical choice for introductory functional analysis courses.
Quick quotes
The reviewer appreciates the concise yet comprehensive coverage of functional analysis in Barbara MacCluer's book, noting its suitability for beginners in graduate studies.
They highlight the inclusion of complex analysis and operator theory, though they question the necessity of concrete Hilbert space examples.
The reviewer finds Barbara MacCluer's 'Elementary Functional Analysis' to be a valuable addition to the field, particularly for its concise yet thorough treatment of the subject.