Operator Theory on One-Sided Quaternion Linear Spaces (eBook)

Intrinsic $S$-Functional Calculus and Spectral Operators

Jonathan Gantner (Autor)

eBook Download: PDF

101 Seiten
American Mathematical Society (Verlag)
978-1-4704-6393-9 (ISBN)

Infos

Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-4704-6393-8 / 1470463938
• ISBN-13: 978-1-4704-6393-9 / 9781470463939