Martínez Ansemil, José MaríaFloret, Klaus2023-06-202023-06-2019880039-3223https://hdl.handle.net/20.500.14352/57618An 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.engjournal articlehttp://webmail.impan.gov.pl/sm/http://webmail.impan.gov.pl/open access515.1Symmetric tensor productsContinuous n-homogeneous polynomialsTensor topologiesTopología1210 Topología