Group algebras and multipliers

We propose a research program with interests in operator algebras, operator spaces, abstract harmonic analysis and operator theory. The main aim of the proposal is the study of Banach algebras associated to groups such as the Fourier algebra A(G), the Beurling-Fourier algebra A_w(G) and the group C*-algebras with particular focus on their spectral properties and multipliers. Many topological and geometrical properties of locally compact groups are reflected on algebraic properties of elements of the algebras associated to groups. One of the aim of the project is to find further interplay between these obejcts. Another goal revolves around questions about Schur multipliers, their unbounded generalizations and Schur multipliers of von Neumann algebras as well as their applications to muliplier problem in harmonic analysis, perturbation theory and theory of operators.