International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 63808, 15 pages
Schur Algebras over -Algebras
1Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10700, Thailand
2Department of Mathematics, Central Michigan University, Mt. Pleasant 48859, MI, USA
3Department of Mathematics, Nanjing University, Nanjing 210029, China
Received 15 November 2006; Accepted 21 May 2007
Academic Editor: Aloys Krieg
Copyright © 2007 Pachara Chaisuriya et al. 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.
Let be a -algebra with identity , and let
denote the set of all states on . For , denote by the set of all infinite matrices over such that the matrix defines a bounded linear operator from to for all . Then is a Banach algebra with the Schur product operation and norm
. Analogs of Schatten's theorems on dualities among the compact
operators, the trace-class operators, and all the bounded operators on
a Hilbert space are proved.