Adji, Sriwulan; Hosseini, Abbas The partial-isometric crossed products of \(c_{0}\) by the forward and backward shifts. (English) Zbl 1206.46056 Bull. Malays. Math. Sci. Soc. (2) 33, No. 3, 487-498 (2010). Summary: Let \((A, \alpha )\) be a system consisting of a \(C^*\)-algebra \(A\) and an extendible endomorphism \(\alpha \) on \(A\). We consider the partial-isometric crossed product \(A \times _{\alpha } \mathbb N\) generated by a copy of \(A\) and a power partial isometry. We show that, for an extendible \(\alpha \)-invariant ideal \(I\) in \(A\), the quotient \((A \times _{\alpha } \mathbb N)/(I \times _{\alpha } \mathbb N)\) of partial-isometric crossed products is isomorphic to the partial-isometric crossed product \(A/I \times _{\bar {\alpha }} \mathbb N\) of the quotient algebra. Then, we use this to give concrete descriptions of the partial-isometric crossed products of \(c_{0}\) by the forward shift and the backward shift. Cited in 2 Documents MSC: 46L55 Noncommutative dynamical systems 06F15 Ordered groups 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47L60 Algebras of unbounded operators; partial algebras of operators Keywords:\(C^*\)-algebra; endomorphism; covariant representation; crossed product PDFBibTeX XMLCite \textit{S. Adji} and \textit{A. Hosseini}, Bull. Malays. Math. Sci. Soc. (2) 33, No. 3, 487--498 (2010; Zbl 1206.46056) Full Text: EuDML Link