Zhidong Pan

Algebraic reflexivity of linear transformations

Let L(U, V) be the set of all linear transformations from U to V, where U and V are vector spaces over a field F. We show that every n-dimensional subspace of L(U, V) is algebraically [√2n]-reflexive, where [ t ] denotes the largest integer not exceeding t, provided n is less than the cardinality of F.

Jordan and Jordan higher all-derivable points of some algebras

In this article, we characterize Jordan derivable mappings in terms of the Peirce decomposition and determine Jordan all-derivable points for some general bimodules. Then we generalize the results to the case of Jordan higher derivable mappings. An immediate application of our main results shows that for a nest 𝒩 on a Banach space X with the associated nest algebra alg 𝒩, if there exists a non-trivial element in 𝒩 that is complemented in X, then every C ∈ alg 𝒩 is a Jordan all-derivable point of L(alg 𝒩, B(X)) and a Jordan higher all-derivable point of L(alg 𝒩).