Hyponormality and subnormality of block Toeplitz operators
2014.07.23 11:42
| 실적년도 | 2012년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Raul E. Curtoa, In Sung Hwang, Woo Young Lee |
| 학술지명 | Advances in Mathematics |
| 권(Vol.) | 230 |
| 호(No.) | 4-6 |
| 게재년월 | 2012년 7월 |
| Impact Factor | |
| SCI 등재 | YES |
| 비고 |
In this paper, we are concerned with hyponormality and subnormality of block
Toeplitz operators acting on the vector-valued Hardy space HCn2 of the unit
circle. First, we establish a tractable and explicit criterion on the
hyponormality of block Toeplitz operators having bounded type symbols via the
triangularization theorem for compressions of the shift operator. Second, we
consider the gap between hyponormality and subnormality for block Toeplitz
operators. This is closely related to Halmos's Problem5: Is every subnormal
Toeplitz operator either normal or analytic? We show that if Φ is a
matrix-valued rational function whose co-analytic part has a coprime
factorization then every hyponormal Toeplitz operator T Φ whose
square is also hyponormal must be either normal or analytic. Third, using the
subnormal theory of block Toeplitz operators, we give an answer to the following
"Toeplitz completion" problem: find the unspecified Toeplitz entries of the
partial block Toeplitz matrix A= so that A becomes subnormal, where U is the
unilateral shift on H 2.
