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• W2116768493 abstract "For a bounded analytic function, ƒ, on the unit disk, D, let Tƒ and Mƒ denote the operators of multiplication by ƒ on H2(∂D) and L2(∂D), respectively. In their 1973 paper, Deddens and Wong asked whether there is an analytic Toeplitz operator Tƒ that commutes with a nonzero compact operator, and whether every operator that commutes with an analytic Toeplitz operator has an extension that commutes with the corresponding multiplication operator on L2. In the first part of this paper, we give an explicit example of an analytic Toeplitz operator Tφ that settles both of these questions. This operator commutes with a nonzero compact operator (a composition operator followed by an analytic Toeplitz operator). The only operators in the commutant of Tφ that extend to commute with Mφ are analytic Toeplitz operators. Although the commutant of Tφ contains more than just analytic Toeplitz operators, Tφ is irreducible. The remainder of the paper seeks to explain more fully the phenomena incorporated in this example by introducing a class of analytic functions, including the function φ, and giving additional conditions on functions g in the class to determine whether Tg commutes with nonzero compact operators, whether Tg is irreducible, and which operators in the commutant of Tg extend to the commutant of Mg. In particular, we find representations for operators in the commutant and second commutant of Tg." @default.
• W2116768493 created "2016-06-24" @default.
• W2116768493 creator A5010703644 @default.
• W2116768493 date "1980-04-01" @default.
• W2116768493 modified "2023-09-23" @default.
• W2116768493 title "An analytic Toeplitz operator that commutes with a compact operator and a related class of Toeplitz operators" @default.
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• W2116768493 doi "https://doi.org/10.1016/0022-1236(80)90098-1" @default.
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