Derivations on Toeplitz Algebras

作者：Didas Michael^*; Eschmeier Joerg

来源：Canadian Mathematical Bulletin, 2014, 57(2): 270-276.

DOI：10.4153/CMB-2013-001-9

• derivations
• Toeplitz algebras
• strictly pseudoconvex domains

Let H-2(Omega) be the Hardy space on a strictly pseudoconvex domain Omega subset of C-n, and let A subset of L-infinity(partial derivative Omega) denote the subalgebra of all L-infinity-functions f with compact Hankel operator H-f. Given any closed subalgebra B subset of A containing C(partial derivative Omega), we describe the first Hochschild cohomology group of the corresponding Toeplitz algebra J(B) subset of B(H-2(Omega)). In particular, we show that every derivation on J(A) is inner. These results are new even for n = 1, where it follows that every derivation on J(H-infinity + C) is inner, while there are non-inner derivations on J(H-infinity + C(partial derivative B-n)) over the unit ball B-n in dimension n %26gt; 1.

• 出版日期2014-6