Affiliations: Department of Mathematics, Faculty of Science, University of Malta, Msida MSD 2080, Malta. david.buhagiar@um.edu.mt; emanuel.chetcuti@um.edu.mt | Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia | Department of Algebra and Geometry, Faculty of Sciences, Palacký University, tř. 17. listopadu 1192/12, CZ-771 46 Olomouc, Czech Republic. dvurecen@mat.savba.sk
Note: [] Dedicated to Prof. Gianpiero Cattaneo on the occasion of his 70th birthday.
Note: [] Address for correspondence: Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, SK-814 73 Bratislava, Slovakia A.D. thanks for the support by Center of Excellence SAS - Quantum Technologies -, ERDF OP R&D Projects CE QUTE ITMS 26240120009 and meta-QUTE ITMS 26240120022, the grant VEGA No. 2/0032/09 SAV and by CZ.1.07/2.3.00/20.0051 and MSM 6198959214.
Abstract: In the Eighties G. Cattaneo contributed to Hilbert space quantum mechanics models using the family of splitting subspaces of an inner product space in order to find completeness criteria. In this paper we show how that theory was developed in the last 25 years into a rich theory which has a close connection to quantum information. G. Cattaneo also posed an open problem which was solved only this year.
