2022/09/20 by Jiankui Li, Li, Jiankui, Shaoze Pan +3
Computer Science · Mathematics · #46H70 #47B48 #47L35 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2209.09523
openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L be a completely distributive commutative subspace lattice or a subspace lattice with two atoms, we use a unified approach to study the derivations, homomorphisms on Alg L. We verify that the multiplier algebra of Alg L∩ K(H) is isomorphic to Alg L and Alg L is zero product determined. For T in Mn(ℂ), n≥ 2, we show that AT is zero product determined if and only if every local derivation from AT into any Banach AT-bimodule is a derivation. In addition, we establish some equivalent conditions for an algebra to be zero product determined. For countable dimensional locally matrix algebras and triangular UHF algebras, we also show that they are zero Lie product determined.