Maps preserving the joint numerical radius distance of operators

Denote the joint numerical radius of an m-tuple of bounded operators A=(A1,…,Am) by w(A). We give a complete description of maps f satisfying w(A-B)=w(f(A)-f(B)) for any two m-tuples of operators A=(A1,…,Am) and B=(B1,…,Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A.