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Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.
List of contents
- 1: Hilbert Spaces
- 2: Diagonal Operators
- 3: Infinite Matrices
- 4: Two Multiplication Operators
- 5: The Unilateral Shift
- 6: The Cesàro Operator
- 7: The Volterra Operator
- 8: Multiplication Operators
- 9: The Dirichlet Shift
- 10: The Bergman Shift
- 11: The Fourier Transform
- 12: The Hilbert Transform
- 13: Bishop Operators
- 14: Operator Matrices
- 15: Constructions with the Shift Operator
- 16: Toeplitz Operators
- 17: Hankel Operators
- 18: Composition Operators
- 19: Subnormal Operators
- 20: The Compressed Shift
About the author
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.
Summary
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.
Additional text
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.
