A Spectral Theory Of Noncommuting Operators

2024
ISBN: 978-3-031-51604-7
Verlag: Springer Nature Switzerland

Buch, Englisch, 272 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 594 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Yang, Rongwei

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.