Gleason’s problem, rational functions and spaces of left-regular functions: The split-quaternion setting

Daniel Alpay, María E. Luna-Elizarrarás, Michael Shapiro, Daniele Struppa

Research output: Contribution to journalArticle

1 Scopus citations


© 2018, Hebrew University of Jerusalem. We study Gleason’s problem, rational functions and spaces of regular functions in the setting of split-quaternions. There are two natural symmetries in the algebra of split-quaternions. The first symmetry allows to define positive matrices with split-quaternionic entries, and also reproducing Hilbert spaces of regular functions. The second leads to reproducing kernel Krein spaces.
Original languageAmerican English
Pages (from-to)319-349
Number of pages284
JournalIsrael Journal of Mathematics
StatePublished - 1 Jun 2018
Externally publishedYes


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