12 Jul
2025
On BSE (BED)-property of Complex Product Banach algebras
Authors :- KG Rachchh
Publication :- Indian Journal of Pure and Applied Mathematics (Springer), 2025
Consider , a commutative Banach algebra, and , a closed ideal in . Then is a commutative Banach algebra with linear operations, multiplication defined as and the norm for all . This particular Banach algebra is denoted as , and we refer to it as the complex product Banach algebra. In the case where is a spectral synthesis ideal in , we establish a critical equivalence: is a BSE-algebra if and only if itself is a BSE-algebra. Similarly, the algebra qualifies as a BED-algebra precisely when is a BED-algebra.