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Room P3.10, Mathematics Building
Michael Stessin, State University of New York, Albany
Subalgebras dense in Hardy spaces
Let be a subalgebra of . For each the Hardy space in the unit disk has a structure of -module. The problem of describing the lattice of closed submodules of this module gives an example of the lattice of closed subspaces invariant under the action of a family of commuting operators. The investigation of the module structure of the disk-algebra was initiated by Wermer in 1950s. It leads to Beurling type results and includes the classical theorem of Beurling as a special case corresponding to the subalgebra of all polynomials. In particular, if the algebra is dense in all , , every closed submodule is -invariant in a weak sense, and if is weak- dense in , then every closed -submodule of is -invariant. In the talk we will discuss some recent results in this area.