In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map between C-algebras, with both and its inverse 1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C-algebras with Hausdorff spectrum, and in general, some special C-algebras associated to continuous fields of C-algebras.
In this paper, let E be a reflexive and strictly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We consider the hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in E. We prove the strong convergence of this method to a common fixed point of the infinite family of nonexpansive mappings, which solves a variational inequality on their common fixed point set. We also give a weak convergence theorem for the hybrid viscosity approximation method involving an infinite family of nonexpansive mappings in a Hilbert space. MSC:47H17, 47H09, 47H10, 47H05.
Let X, Y be realcompact spaces or completely regular spaces consisting of X, Y -points. Let X, Y be a linear bijective map from X, Y (resp. X, Y ) onto X, Y (resp. X, Y ). We show that if X, Y preserves nonvanishing functions, that is,
In this paper, we give a complete description of the structure of zero product and orthogonality preserving linear maps between W*-algebras. In particular, two W*-algebras are *-isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions. It is also the case when they have equivalent linear and left (right) ideal structures.