Matrix characterizations of Lipschitz operators on Banach spaces over Krull valued fields

Abstract

Let $K$ be a complete infinite rank valued field and $E$ a $K$-Banach space with a countable orthogonal base. In [9] and [10] we have studied bounded (called Lipschitz) operators on $E$ and introduced the notion of a strictly Lipschitz operator. Here we characterize them, as well as compact and nuclear operators, in terms of their (infinite) matrices. This results provide new insights and also useful criteria for constructing operators with given properties.