2022/07/17 by Samir Panja, Panja, Samir
Mathematics · #Holomorphic and Operator Theory #Advanced Topics in Algebra #Algebraic and Geometric Analysis
paper · pdf · doi:10.48550/arxiv.2207.08183
In this article, by considering T=(T1,…, Td), an d-tuple of commuting contractions on a Hilbert space H, we study T-Toeplitz operators which consists of bounded operators X on H such that Ti^*XTi=X for all i=1,…,d. We show that any positive T-Toeplitz operator can be factorized in terms of an isometric pseudo-extension of T. A similar factorization result is also obtained for positive pure lower T-Toeplitz operators. However, the latter factorization is obtained in terms of a special type of isometric pseudo-extension of T, and a certain difference has been observed between the case d=2 and d>2. In a more general context, by considering d-tuples of commuting contractions S and T, we also study (S, T)-Toeplitz operators.