Abstract
A JSL algebra is a reflexive algebra with the $${\mathcal {J}}$$ -subspace lattice and a standard subalgebra of it is a subalgebra of it containing all finite rank operators in it. We prove that every local Lie derivation of a JSL algebra is a Lie derivation, every 2-local derivation of a standard subalgebra of a JSL algebra is a derivation and every surjective 2-local isomorphism between standard subalgebras of JSL algebras is an isomorphism. These results can apply to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.
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