(m,n)-Jordan derivations

A subspace lattice L on H is called commutative subspace lattice if all projections in L commute pairwise. It is denoted by CSL. If L is a CSL, then algL is called a CSL algebra. Under the assumption m + n ? 0 where m,n are fixed integers, if ? is a mapping from L into itself satisfying the condition (m + n)?(A2) = 2m?(A)A + 2nA?(A) for all A?A, we call ? an (m,n) Jordan derivation. We show that if ? is a norm continuous linear (m,n) mapping from A into it self then ? is a (m,n)-Jordan derivation.

The Tensor Product Formula for Reflexive Subspace Lattices

We give a characterisation of where and are subspace lattices with commutative and either completely distributive or complemented. We use it to show that Lat is a CSL algebra with a completely distributive or complemented lattice and is any operator algebra.