GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces

Given a real (finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product, we consider the Lorentz cone linear complementarity problem, denoted by LCP(T, Omega, q), where T is a continuous linear operator on H, Omega subset of H is a Lorentz cone, and q is an element of H. We investigate some conditions for which the problem concerned has a unique solution for all q is an element of H (i.e., T has the GUS-property). Several sufficient conditions and several necessary conditions are given. In particular, we provide two sufficient and necessary conditions of T having the GUS-property. Our approach is based on properties of the Jordan product and the technique from functional analysis, which is different from the pioneer works given by Gowda and Sznajder (2007) in the case of finite-dimensional spaces.