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- Title
A Class of Zero Product Determined Banach Algebras.
- Authors
Li, Jiankui; Pan, Shaoze; Su, Shanshan
- Abstract
The primary objective of this paper is to establish the property of zero product determinacy for the algebra Alg L , where L is either a completely distributive commutative subspace lattice or a subspace lattice with two atoms. This objective is achieved by employing a technical approach that involves demonstrating the isomorphism between the multiplier algebra of the algebra consisting of compact operators belonging to Alg L and Alg L . Furthermore, we investigate the properties of derivations and homomorphisms on these algebras as an application of our main result. Additionally, we prove that in the finite-dimensional case, a unital algebra generated by a single operator is zero product determined if and only if every local derivation from the algebra to any of its Banach bimodules is a derivation.
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2024, Vol 47, Issue 1, p1
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-023-01625-9