Abstract
Techniques of Olin and Thomson and of Chevreau, Pearcy and Shields are used to prove the following: If T is an injective weighted shift on H with r(T)=‖T‖ then for each L ∈ (a(T), weak-*)*, there exist f, g ∈ H so that L(A)=◃Af, g▹ for all A ∈a(T). Thus the map i(A)=A is a homeomorphism from (a(T), weak-*) onto (a(T), WOT).
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Miller, T.L. Algebras generated by a weighted shift. Integr equ oper theory 8, 63–74 (1985). https://doi.org/10.1007/BF01199982
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DOI: https://doi.org/10.1007/BF01199982