실적년도 | 2014년 |
---|---|
논문구분 | 국외 |
총저자 | Ra´ul E. Curto, In Sung Hwang, Dong-O Kang and Woo Young Lee |
학술지명 | Advances Mathematics |
권(Vol.) | 255 |
호(No.) | |
게재년월 | 2014년 4월 |
Impact Factor | 1.353(jcr2013) |
SCI 등재 | SCI |
비고 |
•실적년도 : 2014
•논문구분 : 국외
•총 저자 : Ra´ul E. Curto, In Sung Hwang, Dong-O Kang and Woo Young Lee
•학술지명 : Advances Mathematics
•권(Vol.) : 255
•게재년월 : 2014년 4월
•IF : 1.353(jcr2013)
•SCI 등재 : SCI
•국제공동연구 논문여부 : X
•In this paper we deal with the subnormality and the quasinormality of Toeplitz
operators with matrix-valued rational symbols. In particular, in view of Halmos’s Problem 5,
we focus on the question: Which subnormal Toeplitz operators are normal or analytic ? Firstly,
we prove that: Let Φ ∈ L
∞
Mn
be a matrix-valued rational function having a “matrix pole,” i.e.,
there exists α ∈ D for which ker HΦ ⊆ (z −α)H2
Cn , where HΦ denotes the Hankel operator with
symbol Φ. If
(i) TΦ is hyponormal;
(ii) ker [T
∗
Φ, TΦ] is invariant for TΦ,
then TΦ is normal. Hence in particular, if TΦ is subnormal then TΦ is normal. Secondly, we
show that every pure quasinormal Toeplitz operator with a matrix-valued rational symbol is
unitarily equivalent to an analytic Toeplitz operator.
Subnormal and quasinormal Toeplitz operators with matrix-valued rational symbols.pdf