On the theory of infinite-dimensional superspace: reflexive Banach supermodules

A study is made of reflexive Banach supermodules of sequences of elements of a supercommutative Banach superalgebra. The theory of Hilbert supermodules, introduced as isomorphic to the supermodule $l_2(\Lambda)$, is of greatest interest for applications. An analogue of the Riesz theorem on representation of a continuous $\Lambda$-linear functional is proved for Hilbert supermodules.