Canadian mathematical bulletin | |
Derivations on Toeplitz Algebras | |
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
【 预 览 】
Files | Size | Format | View |
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RO201912050577037ZK.pdf | 18KB | download |