Linear and Multilinear Algebra and Function Spaces

Linear reserver problems demand the characterization of linear maps between algebras that leave invariant certain properties or certain subsets or relations. One of the most intractable unsolved problems is Kaplansky's conjecture: every surjective unital invertibility preserving linear map between two semisimple Banach algebras is a Jordan homomorphism. Recently, there has been an upsurge of interest in nonlinear preservers, where the maps studied are no longer assumed linear but instead a weak algebraic condition is somehow involved through the preserving property.

This volume contains several articles on various aspects of preservers, including such topics as Jordan isomorphisms, Aluthge transform, joint numerical radius on C

∗

C∗-algebras, advertible complete algebras, and Gelfand-Mazur algebras. The volume also contains a survey on recent progress on local spectrum-preserving maps.

Several articles in the volume present results about weighted spaces and algebras of holomorphic or harmonic functions, including biduality in weighted spaces of analytic functions, interpolation in the analytic Wiener algebra, and weighted composition operators on non-locally convex weighted spaces.