On the generalized Hyers-Ulam stability of module left derivations |
| |
Authors: | Yong-Soo Jung |
| |
Institution: | Department of Mathematics, Sun Moon University, Asan, Chungnam 336-708, Republic of Korea |
| |
Abstract: | Let A be a unital normed algebra and let M be a unitary Banach left A-module. If f:A→M is an approximate module left derivation, then f:A→M is a module left derivation. Moreover, if M=A is a semiprime unital Banach algebra and f(tx) is continuous in t∈R for each fixed x in A, then every approximately linear left derivation f:A→A is a linear derivation which maps A into the intersection of its center Z(A) and its Jacobson radical rad(A). In particular, if A is semisimple, then f is identically zero. |
| |
Keywords: | Module left derivation Approximate module left derivation Stability |
本文献已被 ScienceDirect 等数据库收录! |
|