Atlas: Tensor products of locally $m-$convex $H^*-$algebras. Structure theorems by Marina Haralampidou

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Tensor products of locally m-convex H^*-algebras. Structure theorems
by
Marina Haralampidou
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, GREECE

F. Murray and J. Von Neumann defined a tensor product of Hilbert spaces, which is a Hilbert space too (1936). In 1964, L. Grove considered the respective tensor product, in the case when the Hilbert spaces are in particular, classical H^*-algebras of W. Ambrose (1946).

In this work we consider tensor products of locally m-convex H^*-algebras. In particular, we prove that the tensor product of two Hausdorff locally m-convex H^*-algebras is an algebra of the same type, when it is equipped with the projective tensor product topology. The existence of an orthogonal basis in a tensor product algebra, as before, is crucial for its structure. So, we examine conditions under which there is such a basis. Based on this, we obtain, among other things, a decomposition reminicent of the second Wedderburn structure theorem.

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Date received: November 29, 1999