Isometries of a generalized tridiagonal algebras $A^{(m)}_{2n}$

Abstract

Let $A_{2n}^{(m)}$ be a generalization of a tridiagonal algebra which is defined in the introduction. In this paper it is proved that if $\varphi;A_{2n}^{(m)}\rightarrow A_{2n}^{(m)}$ is a surjective isometry, then there exists a unitary operator $U$ such that $\varphi(A)=U^{*}AU$ for all $A$ in $A_{2n}^{(m)}$ or a unitary operator $W$ such that $\varphi(A)=W^{l}AW^{*}$ for all $A$ in $A_{2n}^{(m)}$, where ${}^{t}A$ is the transpose matrix of $A$.