Joint m-quasihyponormal operators on a Hilbert space

In this paper, We introduce a new class of multivariable operators known as joint m-quasihyponormal tuple of operators. It is a naturel extension of joint normal and joint hyponormal tuples of operators. An m-tuple of operators S = (S-1,..., S-m) is an element of B(H)(m) is said to be joint m-quasihyponormal tuple if S satisfying Sigma(1 <= l, k <= m) < S*(k)[S*(k), S-l]S(l)u(k) vertical bar u(l) > >= 0, for each finite collections (u(l))(1 <= l <= m) is an element of H. Some properties of this class of multivariable operators are studied.