Generalized derivations on certain Banach algebras
Ali Ebrahimzadeh Esfahani, Mehdi Nemati

TL;DR
This paper investigates the behavior of derivations and generalized derivations on specific Banach algebras, especially those related to group algebras, revealing conditions under which these mappings target the radical of the algebra.
Contribution
It characterizes when derivations and generalized derivations map into the radical for certain Banach algebras, including applications to Fourier algebras of discrete amenable groups.
Findings
Derivations map into the radical under specified conditions.
Necessary and sufficient conditions for the square of a generalized derivation to remain generalized.
Applications to the structure of Fourier algebras of discrete amenable groups.
Abstract
Let be a Banach algebra with the properties that and the algebra is commutative. We show that a derivation of maps into . Using this, we determine among other things when a generalized derivation of maps into . We also study -centralizing generalized derivations of . Then, for a generalized derivation of we obtain a necessary and sufficient condition for to be still a generalized derivation of . The main applications are concerned with the algebras over locally compact groups. In particular, we deduce these results for bidual of Fourier algebras of discrete amenable groups as an application of…
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Algebraic structures and combinatorial models
