# Journal of Operator Theory

Volume 81, Issue 2, Spring 2019  pp. 371-405.

$C^*$-Algebras for partial product systems over $\mathbb{N}$

Authors:  Ralf Meyer (1), Devarshi Mukherjee (2)
Author institution:(1) Mathematisches Institut, Universitaet Goettingen, Bunsenstrasse 3-5, 37073 Goettingen, Germany
(2) Mathematisches Institut, Universitaet Goettingen, Bunsenstrasse 3-5, 37073 Goettingen, Germany

Summary: We define partial product systems over $\mathbb N$. They generalise product systems over $\mathbb N$ and Fell bundles over $\mathbb Z$. We define Toeplitz $C^*$-algebras and relative Cuntz-Pimsner algebras for them and show that the section $C^*$-algebra of a Fell bundle over $\mathbb Z$ is a relative Cuntz-Pimsner algebra. We describe the gauge-invariant ideals in the Toeplitz $C^*$-algebra.

DOI: http://dx.doi.org/10.7900/jot.2018feb20.2213
Keywords: product system, Fell bundle, $C^*$-correspondence, Cuntz-Pimsner algebra, Toeplitz algebra