This article is cited in 2 papers

On the extension of the Toeplitz algebra

T. A. Grigoryan, E. V. Lipacheva, V. A. Tepoyan

Kazan State Power Engineering University

Abstract: We study the $C^*$-extensions of the Toeplitz algebras with the assistance of isometric operators. It is shown that in the case when the Toeplitz algebra acts irreducibly, all such $C^*$-extensions generate the same algebra, i.e., there is no non-trivial extension of the Toeplitz algebra. We provide the examples of the non-trivial extensions of the Toeplitz algebra in the case when its representation is reducible.

Keywords: inverse semigroup, inverse representation, Toeplitz algebra, $\pi$-extension, inverse $\pi$-extension, $C^*$-algebra.

UDC: 517.98

Received: 28.09.2012