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Operator Theory on One-Sided Quaternion Linear Spaces

Jonathan Gantner
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      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.
      Format: Paperback / softback CONTRIBUTORS: Jonathan Gantner EAN: 9781470442385 COUNTRY: United States PAGES: WEIGHT: 210 g HEIGHT: 0 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2021-07-01 CITY: GENRE: MATHEMATICS / Mathematical Analysis WIDTH: 0 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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      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.
      Format: Paperback / softback CONTRIBUTORS: Jonathan Gantner EAN: 9781470442385 COUNTRY: United States PAGES: WEIGHT: 210 g HEIGHT: 0 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2021-07-01 CITY: GENRE: MATHEMATICS / Mathematical Analysis WIDTH: 0 cm SPINE:

      Book Themes:

      Calculus and mathematical analysis

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