Factoring positive operators on reproducing kernel Hilbert spaces
1996
We characterize when positive operators can be factored by “analytic Toeplitz” type operators. As a corollary, we give an operator theory characterization of those invariant subspaces of doubly commuting unilateral shifts, which are generated by a single inner function on the bidisk. The last result extends to shifts of arbitrary (countable) multiplicity.
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