Deddens Algebras and Shift |
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Authors: | Srdjan Petrovic |
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Institution: | 1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA
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Abstract: | We consider Deddens algebras associated to operators of the form S−λI, where S is the unilateral shift and λ is a complex number. We show that such an algebra properly contains the commutant of S and that it is always weakly dense in L(H){{\mathcal L}({\mathcal H})}. Yet, it contains no rank one operators, unless λ = 0, in which case it equals L(H){{\mathcal L}({\mathcal H})}. |
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