  Let $T_n^d(A)$ denote a partial upper triangular operator matrix whose
diagonal entries are given and the others unknown. In this article we have aim
to find characterizations of (left,right) invertibility of $T_n^d(A)$ in terms
of diagonal entries solely, and hence we provide statements which generalize
and correct results of Zhang S., Wu Z. (2012). We pose our results without
invoking separability condition, thus improving results of Zhang S., Wu Z.
(2012), and we give appropriate n-dimensional analogues without assuming
separability as well. We recover many perturbation results of Djordjevi\'c D.
S. (2002), and obtain some results of Du H. K., Pan J. (1994) and Han J. K.,
Lee H. Y., Lee W. Y. (2000) in the case of the Hilbert space setting.
