International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 167-178
Compact Hermitian operators on projective tensor
products of Banach algebras
Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
Received 24 February 2000
Copyright © 2002 T. K. Dutta 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 and be, respectively, an infinite- and a
finite-dimensional complex Banach algebras, and let
be their projective tensor product. We prove
that (i) every compact Hermitian operator on gives rise to a compact Hermitian operator on having the properties that and ;
(ii) if and are separable and has
Hermitian approximation property , then is also separable and has ;
(iii) every compact analytic semigroup on induces the existence of a on having some nice properties. In addition, the converse of the above results are discussed and some open problems are posed.