Which subnormal Toeplitz operator are either normal or analytic?
2014.07.23 15:01
| 실적년도 | 2012년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Raul E. Curto, In Sung Hwang, and Woo Young Lee |
| 학술지명 | Journal of Functional Analysis |
| 권(Vol.) | 263 |
| 호(No.) | 8 |
| 게재년월 | 2012년 10월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos's Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamse's theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two bounded analytic functions), whose analytic and co-analytic parts have the "left coprime factorization", is normal or analytic. We also prove that the left coprime factorization condition is essential. Finally, we examine a well-known conjecture, of whether every subnormal Toeplitz operator with finite rank self-commutator is normal or analytic.
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