FACTORIZATION ALONG COMMUTATIVE SUBSPACE LATTICES
1996
A positive invertible operatorT is said to be factorable along a commutative subspace latticeL if there is an invertible operatorA inAlgL whose inverse is also inAlgL and such thatT=A*A. We investigate a number of conditions that are equivalent to factorability of a given operator along a latticeL. As a byproduct, we derive a condition that guarantees that the latticeTL, defined as {range(TE) ∶E ∈L} is commutative. Applications are suggested to the particular case of factoringL∞ functions via analytic Toeplitz operators on the polydisc.
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