This article focuses on a recent concept of covariation for processes taking values in a separable Banach space  and a corresponding quadratic variation. The latter is more general than the classical one of Métivier and Pellaumail. Those notions are associated with some subspace  of the dual of the projective tensor product of  with itself. We also introduce the notion of a convolution type process, which is a natural generalization of the Itô process and the concept of -semimartingale, which is a natural extension of the classical notion of semimartingale. The framework is the stochastic calculus via regularization in Banach spaces. Two main applications are mentioned: one related to Clark–Ocone formula for finite quadratic variation processes; the second one concerns the probabilistic representation of a Hilbert valued partial differential equation of Kolmogorov type.