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Operator Theory on One-Sided Quaternion Linear Spaces

Intrinsic S -Functional Calculus and Spectral Operators

Jonathan Gantner author

Format:Paperback

Publisher:American Mathematical Society

Published:30th Mar '21

Should be back in stock very soon

Operator Theory on One-Sided Quaternion Linear Spaces cover

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.

ISBN: 9781470442385

Dimensions: unknown

Weight: 210g

101 pages