Some Basic Results on Banach Dialgebras | Asian Journal of Pure and Applied Mathematics

We define some basic notions in Banach dialgebras and show several full normed dialgebra examples. Some findings of Banach dialgebras, which are functional counterparts of Banach algebras, were also developed. If the square of the differential is an identity mapping, the differential associative algebra is a dialgebra. It is determined whether or not the differential map is an isometric map. It was also demonstrated that in Banach dialebra, the left and right products are continuous. Finally, it is proven that the quotient of a Banach dialgebra by its closed ideal is a Banach dialgebra.

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