%0 Journal Article
%A Ansemil, José María M.
%A Floret, Klaus
%T The symmetric tensor product of a direct sum of locally convex spaces
%D 1988
%@ 0039-3223
%U https://hdl.handle.net/20.500.14352/57618
%X An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle times(tau,delta)(n)(F-1 circle plus F-2) gives a direct proof of a recent result of Diaz and Dineen land generalizes it to other topologies tau) that the n-fold projective symmetric and the n-fold projective "full" tensor product of a Iocally convex space fare isomorphic if E is isomorphic to its square E-2.
%~