Spectral Theory on the S-Spectrum for Quaternionic Operators

• Main Authors: Colombo, Fabrizio (Author, http://id.loc.gov/vocabulary/relators/aut), Gantner, Jonathan (http://id.loc.gov/vocabulary/relators/aut), Kimsey, David P. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Operator Theory: Advances and Applications, 270
• Subjects: Operator theory.; Dynamics.; Ergodic theory.; Functional analysis.; Operator Theory.; Dynamical Systems and Ergodic Theory.; Functional Analysis.

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-function...

Table of Contents:

• Introduction
• Slice hyperholomorphic functions
• The S-spectrum and the S-functional calculus
• Properties of the S-functional calculus for bounded operators
• The S-functional calculus for unbounded operators
• The H1 functional calculus
• The F-functional calculus for bounded operators
• The F-functional calculus for unbounded operators
• Quaternionic operators on a Hilbert space
• Spectral integrals
• The spectral theorem for bounded normal operators
• The spectral theorem for unbounded normal operators
• Spectral theorem for unitary operators
• Spectral Integration in the Quaternionic Setting
• Bounded Quaternionic Spectral Operators.