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Applied Mathematics Research eXpress (2008) Vol. 2008 : article ID abn003, 20 pages, doi:10.1093/amrx/abn003 published on July 3, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Operators That Commute with Slant Toeplitz Operators

Mark C. Ho1 and Mu Ming Wong2

1 Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan
2 Department of Information Technology, Meiho Institute of Technology, Pington, Taiwan

Correspondence: Correspondence to be sent to: hom{at}mail.math.nsysu.edu.tw

Let Formula be a separable Hilbert space and Formula be an orthonormal basis in Formula . A bounded operator Formula is called the slant Toeplitz operator if Formula , where cn is the nth Fourier coefficient of a bounded Lebesgue measurable function {varphi} on the unit circle Formula . It has been shown [9], with some assumption on the smoothness and the zeros of {varphi}, that Formula is similar to either the constant multiple of a shift or to the constant multiple of the direct sum of a shift and a rank one unitary, with infinite multiplicity. These results, together with the theory of shifts (e.g., in [11]), allows us to identify all bounded operators on Formula commuting with such Formula .


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