Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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APPROXIMATELY LOCAL DERIVATIONS ON ℓ1-MUNN ALGEBRAS WITH APPLICATIONS TO SEMIGROUP ALGEBRAS

  • Ahmad Alinejad (College of Farabi University of Tehran) ;
  • Morteza Essmaili (Department of Mathematics Faculty of Mathematical and Computer Science Kharazmi University) ;
  • Hatam Vahdati (Department of Mathematics Faculty of Mathematical and Computer Science Kharazmi University)
  • Received : 2022.12.20
  • Accepted : 2023.04.26
  • Published : 2023.10.31
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Abstract

At the present paper, we investigate bounded approximately local derivations of ℓ1-Munn algebra 𝕄I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if 𝒜B(𝒜, 𝒜*) and B𝒜(𝒜, 𝒜*) are reflexive, then every bounded approximately local derivation from 𝕄I(𝒜) into any Banach 𝕄I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ1(S), where S is a uniformly locally finite inverse semigroup.

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References

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