N. L. Carothers Reihenfolge der Bücher

Focusing on the classical aspects of Banach space theory, this short course covers three key topics: Schauder bases, Lp spaces, and C(K) spaces. It highlights the postwar revival of the field led by notable mathematicians such as James and Lindenstrauss, showcasing their impactful results. A foundational knowledge of functional analysis and some exposure to abstract measure theory is required, along with a basic understanding of topology, although an appendix is provided for necessary topological concepts.

This course in real analysis is directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study.