In this paper we study when the product of two dilations of truncated Toeplitz operators gives a dilation of a truncated Toeplitz operator. We will use an approach established in a recent paper written by Ko and Lee. This approach allows us to represent the dilation of the truncated Toeplitz operator via a 2 $\times$ 2 block operator.
BENDAOUD, ZOHRA and SAOULI, NAFISSA
"On the product of dilation of truncated Toeplitz operators,"
Turkish Journal of Mathematics: Vol. 44:
1, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss1/10