Let £f be a complex number in the closed unit disk D , And H be a separable Hilbert space with the orthonormal basis , say ,£`= {e_n:n=0,1,2,¡K}. A bounded operator T on H is called a £f- Toeplitz operator if <Te_(n+1) ,e_(m+1) >=£f<Te_n ,e_m > (where < , > is inner product on H) The L^2 function £p~ £Ua_n e^in£c with a_n=<Te_0 ,e_n> for n>=0 , and a_n=<Te_n ,e_0 > for n<0 is , on the other hand , called the symbol of T The subject arises naturally from a special case of the operator equation
S^* AS=£fA+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) =£h_ij+ca_ij@a_(2i-1,2j-1) =£s_ij+da_ij ) ¢t,
for all i ,j belong Z , where (p_ij ) ,(q_ij ) ,(£h_ij ) ,(£s_ij ) are bounded matrices on l^2 (Z) and a ,b ,c ,d belong 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 . In this paper , we will determine the spectra of £f- Toeplitz operators with |£f|=1 of finite order, and when the symbols are analytic with C^1 boundary values.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0513111-155732 |
| Date | 13 May 2011 |
| Creators | Chen, Po-Han |
| Contributors | Jyh-Shyang Jeang, Mark C. Ho, Hwa-Long Gau, Chia-Hsin Liu |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0513111-155732 |
| Rights | restricted, Copyright information available at source archive |
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