Algebraic reflexivity of linear transformations

Abstract

Abstract. 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 ndimensional 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.

Locally quasi-nilpotent elementary operators

“…We shall call φ ∈ Eℓ(A, L(X)) locally quasi-nilpotent if φ(x) is quasi-nilpotent for every x ∈ A. [16]. Recall that V (or, equivalently, a basis of V ) is said to be locally linearly dependent if ldim V < dim V .…”