Title page for etd-0709109-013026


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URN etd-0709109-013026
Author Chieh-cheng Li
Author's Email Address No Public.
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Department Applied Mathematics
Year 2008
Semester 2
Degree Master
Type of Document
Language English
Title A simple comparison between the Toeplitz and
the λ -Toeplitz operators
Date of Defense 2009-06-17
Page Count 17
Keyword
  • Toeplitz operator
  • Abstract Let λ be a complex number in the closed unit disc, and H be a separable Hilbert space with the orthonormal basis, say, ε={e_n:n=0,1,2,…}. A bounded operator T on H is called a λ-Toeplitz operator if < Te_{m+1},Te_{n+1} >=λ< Te_m,Te_n > (where <•,•> is the inner product on H).
    The subject arises just recently from a special case of the operator equation S*AS = λA + B, where S is a shift on H, which plays an essential role in finding bounded matrix (a_{ij}) on l^2(Z) that solves the system of equations
    a_{2i,2j} = p_{ij} + aa_{ij}
    a_{2i,2j−1} = q_{ij} + ba_{ij}
    a_{2i−1,2j} = v_{ij} + ca_{ij}
    a_{2i−1,2j−1} = w_{ij} + da_{ij}
    for all i, j ∈ Z, where (p_{ij}), (q_{ij}), (v_{ij}), (w_{ij}) are bounded matrices on l^2(Z) and a, b, c, d ∈C.
    It is also clear that the well-known Toeplitz operators are precisely the solutions of S*AS = A, when S is the unilateral shift. The purpose of this paper is to discuss some basic topics, such as boundedness and compactness, of the λ-Toeplitz operators, and study the similarities and the differences with the corresponding results for the Toeplitz operators.
    Advisory Committee
  • Jen-Chih Yao - chair
  • Mu-ming Wong - co-chair
  • Jyh-Shyang Jeang - co-chair
  • Mark C. Ho - advisor
  • Files
  • etd-0709109-013026.pdf
  • indicate in-campus access only
    Date of Submission 2009-07-09

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