Invariant Subspaces for Certain Tuples of Operators with Applications to Reproducing Kernel Correspondences

摘要

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant subspaces for commuting tuples of operators. In that paper the authors prove Beurling-Lax-Halmos type results for commuting tuples T = (T-1, ... , T-d) of operators that are contractive and pure; that is phi T(I) <= I and phi(n)(T)(I) SE arrow 0 where