Let £f be a complex number in the closed unit disc, 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_{m+1},Te_{n+1} >=£f< Te_m,Te_n > (where <¡E,¡E> is the inner product on H).
The subject arises just recently 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} = 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 £f-Toeplitz operators, and study the similarities and the differences with the corresponding results for the Toeplitz operators.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0709109-013026 |
| Date | 09 July 2009 |
| Creators | Li, Chieh-cheng |
| Contributors | Jen-Chih Yao, Mark C. Ho, Mu-ming Wong, Jyh-Shyang Jeang |
| 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-0709109-013026 |
| Rights | restricted, Copyright information available at source archive |
Page generated in 0.0023 seconds