Abstract

In this article, almost derivation on LMC algebras is introduced. Also, it is proved that every almost derivation(or, surjective almost derivation) $T$ on semisimple LMC $Q$-algebras $\Gamma$ with an additional condition on $\Gamma$ has a closed graph. Moreover, it is derived that every almost derivation(or, surjective almost derivation) $T$ on semisimple commutative(or, non commutative) Fréchet $Q$-algebra $\Gamma$ with an additional condition on $\Gamma$ is continuous. To further illustrate our primary results, an example is provided.

Keywords: LMC-algebra; almost derivation; automatic continuity.

MSC: 46H40, 46H05

DOI: 10.57016/MV-9K9832wr

Pages:  141--146     

Volume  77 ,  Issue  2 ,  2025