Type of some nuclear subalgebras of the Toeplitz algebra generated by the inverse subsemigroups of a bicyclic semigroup - Оvsepyan, K. H. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We construct a $Z$-graded structure of the Toeplitz algebra and consider nuclear $C*$ -subalgebras of the Toeplitz algebragenerated by the inverse subsemigroups of the bicyclic semigroup. The types of these algebras with respect to the Toeplitzalgebra are determined. In addition, it is shown, that considered algebras are equipped with the structrure of Hilbert$C*$ -modules.