Centralizers of image-subspace lattice algebras Original Research Article

Let image be a image-subspace lattice on a Banach space and let image be a subalgebra of Alg image which contains image, where image denotes the algebra of all finite rank operators in image. A left (right) centralizer of image is an additive map image satisfying Φ(AB)=Φ(A)B(Φ(AB)=AΦ(B)) for all image, and a centralizer of image is a both left and right centralizer. In this paper, we describe the general form of a centralizer of image, and show that every linear local left (right) centralizer of image is a left (right) centralizer. Also, it is proved that if a linear map image satisfies Φ(P)=Φ(P)P=PΦ(P) for every idempotent P in image, then phi is a centralizer.