The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood's conjecture to the Banach Tarski paradox have been selected for their mathematical beauty as well as educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst...

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.