Inspired by recent works on m-isometric and n-symmetric multivariables
operators on Hilbert spaces, in this paper we introduce the class of (m,n)-isosymmetric multivariables operators. This new class of operators emerges
as a generalization of the m-isometric and n-isosymmetric multioperators.
We study this class of operators and give some of their basic properties. In
particular, we show that if RβB(d)(H) is an (m,n)-isosymmetric multioperators and QβB(d)(H) is an q-nilpotent multioperators,
then R+Q is an (m+2qβ2,n+2qβ1)-isosymmetric
multioperators under suitable conditions. Moreover, we give some results about
the joint approximate spectrum of an (m,n)-isosymmetric multioperators