Operator theory on one-sided quaternion linear spaces : intrinsic S-functional calculus and spectral operators
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Bibliographic Information
Operator theory on one-sided quaternion linear spaces : intrinsic S-functional calculus and spectral operators
（Memoirs of the American Mathematical Society, no. 1297）
American Mathematical Society, c2020
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"September 2020, volume 267, number 1297 (first of 7 numbers)"
Includes bibliographical reference (p. 97-98) and index
Description and Table of Contents
Description
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.
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