Abstract
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a closed uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.
Keywords
- Inner product spaces
- quaternionic topological vector spaces
- Krein spaces
- quaternionic functional analysis
Mathematics Subject Classification (2010). 47S10, 30G35, 46C20.
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© 2015 Springer International Publishing Switzerland
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Alpay, D., Colombo, F., Sabadini, I. (2015). Inner Product Spaces and Krein Spaces in the Quaternionic Setting. In: Alpay, D., Kirstein, B. (eds) Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes. Operator Theory: Advances and Applications(), vol 244. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10335-8_4
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DOI: https://doi.org/10.1007/978-3-319-10335-8_4
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-10334-1
Online ISBN: 978-3-319-10335-8
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