# A linear map satisfying the given property

by Fermat   Last Updated August 13, 2019 21:20 PM

Let $$A$$ and $$B$$ be two Banach algebras such that $$B$$ is a Banach $$A$$-bimodue and $$T:A\rightarrow B$$ a linear map satisfying $$T(aa')=aT(a')+T(a)a'+T(a)T(a')$$ for all $$a,a'\in A$$.

If the algerba multiplication on $$B$$ is the trivial action, i.e., $$bb'=0$$ for all $$b,b'\in B$$, then $$T$$ is said to be a derivation. If the module actions are as $$ab=ba=0$$, then it is an algerba homomorphism.

Is there a special name for $$T$$ in general? And what are some properties of such mappings?

Tags :

## Related Questions

Updated January 17, 2019 08:20 AM

Updated August 03, 2018 01:20 AM

Updated February 22, 2019 09:20 AM

Updated March 03, 2018 21:20 PM

Updated November 10, 2017 05:20 AM