Kreĭn C*-categories

Abstract

-categories are essentially norm-closed -categories of bounded linear operators between Hilbert spaces. The purpose of this work is to identify suitable axioms defining Kreĭn -categories, i.e. those categories that play the role of -categories whenever Hilbert spaces are replaced by more general indefinite inner product Kreĭn spaces, and provide some basic examples. Finally we provide a Gel'fand-Naĭmark representation theorem for Kreĭn -algebras and Kreĭn -categories.