Linear And Multilinear Algebra And Function Spaces International Conference Algebra And Related Topics Icart 2018 July 25 2018 Mohammed V University Rabat Morocco Contemporary Mathematics A Bourhim Editor by A. Bourhim (editor), J. Mashreghi (editor), L. Oubbi (editor), Z. Abdelali (editor) 9781470446932, 1470446936 instant download after payment.

The International Conference on Algebra and Related Topics (ICART 2018)
was held at Faculty of Sciences, Mohammed V University in Rabat, Morocco, from
July 2 to 5, 2018. It covered various research areas presented in three parallel
sessions. “Linear and Multilinear Algebra, and Function spaces (in short LMAFS)”
was one of them. The topics of interest of this session included linear and nonlinear
preserver problems, Banach algebras, topological algebras, operator theory, and
weighted function spaces. Numerous international experts in these areas presented
their ongoing research, and interacted with their colleagues and Ph.D students
working in their fields.
Linear preserver problems demand the characterization of linear maps between
algebras that leave invariant certain properties or subsets or relations. The earliest
result on linear preserver problems was established by Frobenius in 1896. Frobenius
characterized all bijective linear transformations on the algebra Mn(C) of complex
matrices that preserve the determinant of matrices. His result was generalized in
1925 by Schur for subdeterminants of a fixed order and in 1949 by Dieudonn´e to
arbitrary fields and for linear maps preserving the set of singular matrices. Since
then, various linear preserver problems have been considered and a number of
techniques have been developed to treat them. One of the most intractable unsolved
problems in this active research area is the famous Kaplansky’s conjecture that
asserts that every surjective unital invertibility preserving linear map between two
semisimple Banach algebras is a Jordan homomorphism. This conjecture has not
been fully solved yet and remains open even for general C∗-algebras, but it has
been confirmed, in particular, for von Neumann algebras and for the algebra of all
bounded linear operators on a Banach space.