Journal of the
Korean Mathematical Society JKMS

In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\mathcal L$ is a CDCSL and $\mathcal M$ is a dual normal unital Banach alg$\mathcal L$-bimodule, then every local generalized derivation of above type from alg$\mathcal L$ into $\mathcal M$ is a generalized derivation.

Keywords: Jordan $\tau$-centralizer, local $\tau$-centralizer, local generalized derivation, Hochschild 2-cocycle

MSC numbers: 47B47, 47L35