A Spectral Theory Of Noncommuting Operators

The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.

Studies primarily mathematical and scientific phenomena that involve several interacting elements Useful for analyzing big data that come from multiple channels Written in a didactic manner which includes exercises and research projects

Autorentext

Rongwei Yang ( ) is a professor of mathematics at the University at Albany, the State University of New York. His research interest includes a wide range of fields in mathematics and math physics. Several of his projects have been supported by the National Science Foundation and the Simons Foundation.

Inhalt

1 Characteristic Polynomial in Several Variables.- 2 Finite Dimensional Group Representations.- 3 Finite Dimensional Lie Algebras.- 4 Projective Spectrum in Banach Algebras.- 5 The C-algebra of the Infinite Dihedral Group.- 6 The Maurer-Cartan Form of Operator Pencils.- 7 Hermitian Metrics on the Resolvent Set.- 8 Compact Operators and Kernel Bundles.- 9 Weak Containment and Amenability.- 10 Self-similarity and Julia Sets.- References.