In this article, by considering T=(T₁,..., T_n), an n-tuple of commuting contractions on a Hilbert space H, we study T-Toeplitz operators which consists of bounded operators X on H such that T_i*XT_i=X for all i=1,...,n. We show that any positive T-Toeplitz operator can be factorized in terms of an isometric pseudo-extension of T. A similar factorization result in terms of a BCL type of co-isometric pseudo-extension is also obtained for positive pure lower T-Toeplitz operators. However, a certain difference has been observed between the case n=2 and n>2. In a more general context, by considering n-tuples of commuting contractions S and T, we also study (S, T)-Toeplitz operators.

The author would like to thank his supervisor, Prof. Bata Krishna Das, for introducing him to the problem. The author is also grateful to him for reading the article with his prodigious patience.