On rings and Banach algebras with skew derivations
Abstract
In the present paper, we investigate the commutativity of a prime Banach algebra with skew derivations and prove that if
is prime Banach algebra and
has a nonzero continuous linear skew derivation
from
to
such that
for an integers
and
and sufficiently many
, then
is commutative.
![\Aa](http://212.189.136.205/plugins/generic/latexRender/cache/3aa3fa42d271bbb127da38bf55cec787.png)
![\Aa](http://212.189.136.205/plugins/generic/latexRender/cache/3aa3fa42d271bbb127da38bf55cec787.png)
![\f](http://212.189.136.205/plugins/generic/latexRender/cache/ca15e113508d0f7b0f43949dabfc0108.png)
![\Aa](http://212.189.136.205/plugins/generic/latexRender/cache/3aa3fa42d271bbb127da38bf55cec787.png)
![\Aa](http://212.189.136.205/plugins/generic/latexRender/cache/3aa3fa42d271bbb127da38bf55cec787.png)
![[\f(\xa^{m}), \f(\ya^{n})] - [\xa^{m}, \ya^{n}] \in \z(\Aa)](http://212.189.136.205/plugins/generic/latexRender/cache/6d17e8ccaf6aa5dad4363c503f44b1ac.png)
![m = m(\xa, \ya)>1](http://212.189.136.205/plugins/generic/latexRender/cache/8904b91374836209e49dd96db34bd314.png)
![n = n(\xa, \ya)>1](http://212.189.136.205/plugins/generic/latexRender/cache/1c7c86d36805a0ef0dc70f54b933f8f8.png)
![\xa, \ya](http://212.189.136.205/plugins/generic/latexRender/cache/d0fdec128ed66f24f908cb8572026a26.png)
![\Aa](http://212.189.136.205/plugins/generic/latexRender/cache/3aa3fa42d271bbb127da38bf55cec787.png)
DOI Code:
10.1285/i15900932v40n1p73
Keywords:
Prime Banach algebra; skew derivation
Full Text: PDF