Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword Toeplitz algebras

 Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2013 (vol 57 pp. 270)

Didas, Michael; Eschmeier, Jörg
 Derivations on Toeplitz Algebras Let $H^2(\Omega)$ be the Hardy space on a strictly pseudoconvex domain $\Omega \subset \mathbb{C}^n$, and let $A \subset L^\infty(\partial \Omega)$ denote the subalgebra of all $L^\infty$-functions $f$ with compact Hankel operator $H_f$. Given any closed subalgebra $B \subset A$ containing $C(\partial \Omega)$, we describe the first Hochschild cohomology group of the corresponding Toeplitz algebra $\mathcal(B) \subset B(H^2(\Omega))$. In particular, we show that every derivation on $\mathcal{T}(A)$ is inner. These results are new even for $n=1$, where it follows that every derivation on $\mathcal{T}(H^\infty+C)$ is inner, while there are non-inner derivations on $\mathcal{T}(H^\infty+C(\partial \mathbb{B}_n))$ over the unit ball $\mathbb{B}_n$ in dimension $n\gt 1$. Keywords:derivations, Toeplitz algebras, strictly pseudoconvex domainsCategories:47B47, 47B35, 47L80
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/