This text is the first complete study and monograph dedicated to singular traces. For mathematical readers the text offers, due to Nigel Kalton's contribution, a complete theory of traces on symmetrically normed ideals of compact operators. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to Dixmier traces and the deeper mathematical features of singular traces. An application section explores the consequences of these features, which previously were not discussed in general texts on noncommutative geometry.

This book is the first complete study and monograph dedicated to singular traces. The text mathematically formalises the study of traces in a self contained theory of functional analysis. Extensive notes will treat the historical development. The final section will contain the most complete and concise treatment known of the integration half of Connes' quantum calculus.

Singular traces are traces on ideals of compact operators that vanish on the subideal of finite rank operators. Singular traces feature in A. Connes' interpretation of noncommutative residues. Particularly the...