Local derivation on some class of subspace lattice algebras

2025/01/05 by Hongjie Chen, Liguang Wang, Chen, Hongjie +3
Computer Science · Mathematics · #46L10 #47L75 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2501.02463

openalex publication_date 2025/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a separable Hilbert space and L₀⊂ B(H) a complete reflexive lattice. Let \mathscrK be the direct sum of n₀ copies of H (n₀∈ℕ and n₀≥ 2) or the direct sum of countably infinite many copies of H respectively. We construct two class of subspace lattices L on \mathscrK. Let AlgL be the corresponding subspace lattice algebra. We show that every local derivation from AlgL into B(\mathscrK) is a derivation.

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