Title page for etd-0725111-213522


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URN etd-0725111-213522
Author Chih-Hao Chen
Author's Email Address c932040011@yahoo.com.tw
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Department Applied Mathematics
Year 2010
Semester 1
Degree Master
Type of Document
Language English
Title Fredholm spectra of λ-Toeplitz operators
Date of Defense 2011-01-14
Page Count 14
Keyword
  • Toeplitz operator
  • composition operator
  • λ-Toeplitz operator
  • Abstract 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= {en : n =0 , 1 , 2…}. A bounded operator T on H is called a λ-Toeplitz operator if <Tem+1 , en+1> =λ <Tem , en> (where <•,•> is the inner product on H).If the function φ can be represented as a linear combination of the above orthonormal basis with the coefficients an=<Te0 ,en >, n≥ 0,and an=<Telnl ,e0 >, n<0, then we call this the symbol of T . The subject arises naturally from a special case of the operator equation
    S*AS =λA + B; where S is a shift on H ,
    and in this operator equation the matrix A can solve a special set of simultaneous equations.
    It is also clear that the well-known Toeplitz operators are precisely the solutions of S*AS = A, when S is the unilateral shift.In this paper,we will review the similarities and differences between λ-Toeplitz operators and Toeplitz operators. The main purpose is to generalize the well-known Coburn's characterization for the essential spectrum(or,the same in this case,spectrum)for Toeplitz operators to λ-Toeplitz operators.
    Advisory Committee
  • Chia-Hsin Liu - chair
  • Jyh-Shyang Jeang - co-chair
  • Hwa-Long Gau - co-chair
  • Mark C. Ho - advisor
  • Files
  • etd-0725111-213522.pdf
  • indicate in-campus access only
    Date of Submission 2011-07-25

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