Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have...

Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, and mathematical physics. This text covers the central themes of operator theory. It is suitable for graduate students who have had a standard course in functional analysis.

Includes chapters that cover the basics about subnormal operator theory and present a study of analytic functions on the unit disk. This book includes such topics as: some results on hyponormal operators, a study of weak-star rational approximation, and a set of results that can be termed structure theorems for subnormal operators.

For years, higher education prospered. It loudly proclaimed that college graduates command far greater lifetime incomes. Ample funding followed. We produced. But that argument has begun to sour. A college degree has long since stopped being a guarantee of prosperity or even job security. Society has begun to question its support for universities. In this environment, mathematicians and all academics must begin to change, compete, and seek resources that will be used with greater care. It is the only solution if we hope to maintain the integrity of the enterprise....

Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have...

This is the sequel to my book Functions of One Complex Variable I, and probably a good opportunity to express my appreciation to the mathemat- ical community for its reception of that work. In retrospect, writing that book was a crazy venture. As a graduate student I had had one of the worst learning experiences of my career when I took complex analysis; a truly bad teacher. As a non-tenured assistant professor, the department allowed me to teach the graduate course in complex analysis. They thought I knew the material; I wanted to learn it. I adopted a standard text and shortly after...

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs.Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line.Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent...