Operator Theory on One-Sided Quaternion Linear Spaces : Intrinsic S -Functional Calculus and Spectral Operators (Memoirs of the American Mathematical Society)

Operator Theory on One-Sided Quaternion Linear Spaces : Intrinsic S -Functional Calculus and Spectral Operators (Memoirs of the American Mathematical Society)

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 101 p.
  • 言語 ENG
  • 商品コード 9781470442385
  • DDC分類 512.5

Full 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.