A class of non-symmetric forms on the canonical simplex of $R^d$

We introduce a class of non-symmetric bilinear forms on the $d$-dimensional canonical simplex, related with Fleming-Viot operators. Strong continuity, closedness and results in the spirit of Beurling-Deny criteria are established. Moreover, under suitable assumptions, we prove that the forms satisfy the Log-Sobolev inequality. As a consequence, regularity results for semigroups generated by a class of Fleming-Viot type operators are given.