The Wonders of the Cesàro Operator

This is a survey of the classical Cesàro operator aimed at graduate students as well as more experienced researchers. The eleven chapters of the book cover topics from Cesàro's early work on summability of series and continues with the seminal paper of Brown, Halmos, and Shields on the Cesàro operator. Along the way, various normality classes of the Cesàro operator are covered, as well as invariant subspaces and semigroups. Recent and ongoing work concerning generalizations of the Cesàro operator is also included. The book also features detailed endnotes for each chapter with historical references and suggestions for further reading.