Derivations on Toeplitz Algebras

Canadian mathematical bulletin

Michael Didas¹  Jörg Eschmeier¹ 

[1] Fachrichtung Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany

关键词: derivations;    Toeplitz algebras;    strictly pseudoconvex domains;   

DOI  :  10.4153/CMB-2013-001-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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-innerderivations on $mathcal{T}(H^infty+C(partial mathbb{B}_n))$ overthe unit ball $mathbb{B}_n$ in dimension $ngt 1$.

【 授权许可】

Unknown