Generalized multipliers for left-invertible analytic operators and their applications to commutant and reflexivity
Copyright policy )Generalized multipliers for left-invertible analytic operators and their applications to commutant and reflexivity
We introduce generalized multipliers for left-invertible analytic operators. We show that they form a Banach algebra and characterize the commutant of such operators in its terms. In the special case, we describe the commutant of balanced weighted shift only in terms of its weights. In addition, we prove two independent criteria for reflexivity of weighted shifts on directed trees.
23 pages
47A45, 47B37, Weighted shift on directed tree, Reflexivity, commutant, reflexivity, Canonical models for contractions and nonselfadjoint linear operators, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, generalized multiplier, FOS: Mathematics, Generalized multiplier, weighted shift on directed tree, Commutant
47A45, 47B37, Weighted shift on directed tree, Reflexivity, commutant, reflexivity, Canonical models for contractions and nonselfadjoint linear operators, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Functional Analysis (math.FA), Mathematics - Functional Analysis, generalized multiplier, FOS: Mathematics, Generalized multiplier, weighted shift on directed tree, Commutant
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