Compact linear operators between probabilistic normed spaces

A pair (X, N) is said to be a probabilistic normed space if X is a real vector space, N is a mapping from X into the set of all distribution functions (for x is an element of X, the distribution function N(x) is denoted by N-x, and N-x(t) is the value N-x at t is an element of R) satisfying the following conditions: (N1) N-x(0) = 0, (N2) N-x (t) = 1 for all t > 0 iff x = 0, (N3) N-alpha x(t) = N-x(t/vertical bar alpha vertical bar) for all alpha is an element of R\{0}, (N4) Nx+y(s + t) >= min{N-x(s), N-y(t)} for all x, y is an element of X, and s, t is an element of R-0(+). In this article, we study compact linear operators between probabilistic normed spaces.