Operator Theory by Example

Stephan Ramon Garcia is W. M. Keck Distinguished Service Professor at Pomona College. He is the author of five books and over 100 research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, combinatorics, and other fields. He has served on the editorial boards of the Proceedings of the American Mathematical Society, Notices of the American Mathematical Society, Involve, and The American Mathematical Monthly. He has received five NSF research grants as principal investigator and six teaching awards from three different institutions. He is a Fellow of the AMS and the inaugural winner of the AMS Dolciani Prize for Excellence in Research.Javad Mashreghi completed his doctoral studies at McGill University in 2001 and then joined Laval University, where he promoted to full professorship in 2009. He has worked in numerous committees of CMS (Canadian Mathematical Society), AMS (American Mathematical Society), MCA (Mathematical Congress of Americas), NSERC (Natural Sciences and Engineering Research Council of Canada) and NSF (National Science Foundation). He served as the 35th President of the CMS (2020-2022).William Ross is a graduate of Fordham University (Bronx, New York) and the University of Virginia (Charlottesville, Virginia) and is currently the Roger Francis and Mary Saunders Richardson Professor of Mathematics at the University of Richmond (Richmond, Virginia). He is the author of eight books and 70 papers. He has also served as an editor on several research journals in mathematics.

The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well researched historical facts which place each chapter within the broader context of the development of the field as a whole.

• 1: Hilbert Spaces2: Diagonal Operators3: Infinite Matrices4: Two Multiplication Operators5: The Unilateral Shift6: The Cesàro Operator7: The Volterra Operator8: Multiplication Operators9: The Dirichlet Shift10: The Bergman Shift11: The Fourier Transform12: The Hilbert Transform13: Bishop Operators14: Operator Matrices15: Constructions with the Shift Operator16: Toeplitz Operators17: Hankel Operators18: Composition Operators19: Subnormal Operators20: The Compressed Shift