Note on Derivations of Certain non-CSL Algebras

A subspace lattice $\{(0), M, N, H\}$ of a Hilbert space $H$ is called a generalized generic lattice if $M\cap N =M^\perp\cap N^\perp =(0)$ and $\dim (M^\perp \cap N)=\dim (M\cap N^\perp)$. In this note, we show that each derivation of a generalized generic lattice algebra into itself is inner.