A Spectral Theory Of Noncommuting Operators / by Rongwei Yang.

Format:

Book

Author/Creator:

Yang, Rongwei.

Series:

Mathematics and Statistics Series

Language:

English

Subjects (All):

Functional analysis.

Functional Analysis.

Local Subjects:

Functional Analysis.

Physical Description:

1 online resource (277 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

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.

ISBN:

9783031516054

3031516052

OCLC:

1428779690