Geodesic
On Banach algebras defined by multipliers
Filomat, Tome 36 (2022) no. 17, p. 5945

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DOI

In this paper, we investigate a Banach algebra A T , where A is a Banach algebra and T is a left (right) multiplier on A. We study some concepts on A T such as n-weak amenability, cyclic amenability, biflatness, biprojectivity and Arens regularity. For the group algebra L 1 (G) of an infinite compact group G, it is shown that there is a multiplier T such that L 1 (G) T has not a bounded approximate identity. For ℓ 1 (S), where S is a regular semigroup with a finite number of idempotents, we show that there is a multiplier T such that Arens regularity of ℓ 1 (S) T implies that S is compact.
DOI : 10.2298/FIL2217945E
Classification : 43A07, 43A22, 46H25
Keywords: Arens regularity, multiplier, weak amenability 
Ali Ebadian; Ali Jabbari; Saeid Shams. On Banach algebras defined by multipliers. Filomat, Tome 36 (2022) no. 17, p. 5945 . doi: 10.2298/FIL2217945E
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     author = {Ali Ebadian and Ali Jabbari and Saeid Shams},
     title = {On {Banach} algebras defined by multipliers},
     journal = {Filomat},
     pages = {5945 },
     year = {2022},
     volume = {36},
     number = {17},
     doi = {10.2298/FIL2217945E},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217945E/}
}
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