Extension of (η,φ)-Derivation on the CSL Subalgebra of von Neumann Algebra

Abstract

This article aims to demonstrate the following: consider , a Commutative Subspace Lattice (CSL) subalgebra of a von Neumann algebra acting on a Hilbert space . Suppose that are two linear mappings that satisfy some certain functional identities. Then is a generalized (η, φ)-derivation with associated (η, φ)-derivation in , where η and φ are automorphisms in .