### Title page for etd-0709109-013026

URN etd-0709109-013026 Chieh-cheng Li No Public. This thesis had been viewed 5211 times. Download 2 times. Applied Mathematics 2008 2 Master English A simple comparison between the Toeplitz andthe λ -Toeplitz operators 2009-06-17 17 Toeplitz operator 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 equationsa_{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. Jen-Chih Yao - chair Mu-ming Wong - co-chair Jyh-Shyang Jeang - co-chair Mark C. Ho - advisor indicate in-campus access only 2009-07-09

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