Title page for etd-0704106-163148


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URN etd-0704106-163148
Author Chien-chou Chen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title Operators which are constant with respect to slant Toeplitz operators
Date of Defense 2006-06-29
Page Count 15
Keyword
  • shift
  • constant
  • slant Toeplitz operator
  • Abstract Let H be a separable Hilbert space and {e_n : n belong to Z} be an orthonormal basis in H. A bounded operator T is called the slant Toeplitz operator if <T ej , ei> =c2i−j , where c_n is the n-th Fourier series of a bounded Lebesgue measurable function on the unit circle T = {z belong to C : |z| = 1}. It has been shown [7] that T* is an isometry if and only if |fi(z)|^2 +|fi(−z)|^2 = 2 a.e. on T and if this is the case and fi belong to C(T), then either T is unitarily equivalent to a shift or to the direct sum of a shift and a rank one unitary, with infinite multiplicity
    (for the shift part, that is). Moreover, with some additional assumption on the smoothness and the zeros of fi, T* 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. On the other hand, according to the terminologies in [10], an operator A that is constant with respect to a shift S if AS = SA and A S = SA . Therefore, in this article, we will study the operators that is constant with respect to T , i.e., bounded operator A satisfying AT = T A and A T = T A .
    Advisory Committee
  • Ngai-Ching Wong - chair
  • none - co-chair
  • none - co-chair
  • Mark C. Ho - advisor
  • Files
  • etd-0704106-163148.pdf
  • indicate access worldwide
    Date of Submission 2006-07-04

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