  We generalize three results of M. Aguiar, which are valid for Loday's
dendriform algebras, to arbitrary dendriform algebras, i.e., dendriform
algebras associated to algebras satisfying any given set of relations. We
define these dendriform algebras using a bimodule property and show how the
dendriform relations are easily determined. An important concept which we use
is the notion of polarization of an algebra, which we generalize here to
(arbitrary) dendriform algebras: it leads to a generalization of two of
Aguiar's results, dealing with deformations and filtrations of dendriform
algebras. We also introduce weak Rota-Baxter operators for arbitrary algebras,
which lead to the construction of generalized dendriform algebras and to a
generalization of Aguiar's third result, which provides an interpretation of
the natural relation between infinitesimal bialgebras and pre-Lie algebras in
terms of dendriform algebras. Throughout the text, we give many examples and
show how they are related.
