Additive functionals and operators on a quaternionic Hilbert space. (English) Zbl 0664.46080
It is shown that the structure of functionals and operators on a quaternionic Hilbert space is much richer than is generally appreciated, but one has to work simultaneously with the usual definition and an unusual one of multiplication by scalar for functionals - the different definitions, of course, give rise to different vector spaces. A generalized version of the Riesz representation theorem for quaternionic Hilbert spaces is proved along with the basic theorem on the algebra of additive operators on such a space.
MSC:
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
| 47L30 | Abstract operator algebras on Hilbert spaces |
| 46N99 | Miscellaneous applications of functional analysis |
| 47L90 | Applications of operator algebras to the sciences |
Keywords:
structure of functionals and operators on a quaternionic Hilbert space; multiplication by scalar for functionals; Riesz representation theorem for quaternionic Hilbert spaces; algebra of additive operatorsReferences:
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