Aluthge iterations of weighted translation semigroups |
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Authors: | C. Burnap M. Lee |
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Affiliation: | a Department of Mathematics, UNC Charlotte, Charlotte, NC 28223, USA b Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea |
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Abstract: | The problem whether Aluthge iteration of bounded operators on a Hilbert space H is convergent was introduced in [I. Jung, E. Ko, C. Pearcy, Aluthge transforms of operators, Integral Equations Operator Theory 37 (2000) 437-448]. And the problem whether the hyponormal operators on H with dimH=∞ has a convergent Aluthge iteration under the strong operator topology remains an open problem [I. Jung, E. Ko, C. Pearcy, The iterated Aluthge transform of an operator, Integral Equations Operator Theory 45 (2003) 375-387]. In this note we consider symbols with a fractional monotone property which generalizes hyponormality and 2-expansivity on weighted translation semigroups, and prove that if {St} is a weighted translation semigroup whose symbol has the fractional monotone property, then its Aluthge iteration converges to a quasinormal operator under the strong operator topology. |
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Keywords: | Weighted translation semigroup Aluthge transform Aluthge iteration Hyponormal operator |
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