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This volume contains the proceedings of the International Conference on Algebra and Related Topics, held from July 2-5, 2018, at Mohammed V University, Rabat, Morocco.
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 in 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 $C^*$-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.
Linear and Multilinear Algebra and Function Spaces
C. Boyd and P. Rueda, Biduality in weighted spaces of analytic functions
O. El-Fallah and K. Kellay, Interpolation with functions in the analytic Wiener algebra
L. Molnar, Jordan isomorphisms as preservers
Z. E. Abdelali and H. Nkhaylia, Multiplicatively pseudo spectrum-preserving maps
M. Weigt and I. Zarakas, On algebraic characterizations of advertibly complete algebras
F. Chabbabi and M. Mbekhta, Polar decomposition, Aluthge and mean transforms
A. Bourhim and J. Mashreghi, Recent progress on local spectrum-preserving maps
M. R. Alfuraidan and N. Machrafi, Sadovskii-type fixed point results for edge-preseving mappings
M. Mabrouk, The joint numerical radius on $C^*$-algebras; M. Klilou and L. Oubbi, Weighted composition operators on non locally convex weighted spaces with operator-valued weights
M. Bresar and P. Semrl, Zero product preserving maps on matrix rings over division rings.