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Journal of Mathematics
Volume 2016, Article ID 8301709, 7 pages
http://dx.doi.org/10.1155/2016/8301709
Research Article

Khatri-Rao Products for Operator Matrices Acting on the Direct Sum of Hilbert Spaces

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Chalongkrung Rd., Bangkok 10520, Thailand

Received 2 July 2016; Revised 20 September 2016; Accepted 18 October 2016

Academic Editor: Ralf Meyer

Copyright © 2016 Arnon Ploymukda and Pattrawut Chansangiam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce the notion of Khatri-Rao product for operator matrices acting on the direct sum of Hilbert spaces. This notion generalizes the tensor product and Hadamard product of operators and the Khatri-Rao product of matrices. We investigate algebraic properties, positivity, and monotonicity of the Khatri-Rao product. Moreover, there is a unital positive linear map taking Tracy-Singh products to Khatri-Rao products via an isometry.