Isometries of a generalized tridiagonal algebras A(m)"2n

Let A(m)2n be a generalization of a tridiagonal algebra which is defined in the introduction. In this paper it is proved that if φ: A(m)2n → A(m)2n is a surjective isometry, then there exsits a unitary operator U such that φ(A)=U*AU for all A in A(m)2n or a unitary operator W such that φ(A)=W1AW* for all A in A(m)2n. where A is the transpose matrix of A