  The main purpose of this paper is to present a decomposition theorem for
nonnegative sesquilinear forms. The key notion is the short of a form to a
linear subspace. This is a generalization of the well-known operator short
defined by M. G. Krein. A decomposition of a form into a shorted part and a
singular part (with respect to an other form) will be called short-type
decomposition. As applications, we present some analogous results for bounded
positive operators acting on a Hilbert space; for additive set functions on a
ring of sets; and for representable positive functionals on a $\ast$-algebra.
