Toeplitz算子亚正规性的判别法  

Judgement method of hyponormal Toeplitz operator

作　　者：朱耀亮[1] 陈务深[1] 王成[1] 

机构地区：[1]南京工业大学理学院,江苏南京210009

出　　处：《南京工业大学学报（自然科学版）》2003年第5期57-60,共4页Journal of Nanjing Tech University(Natural Science Edition)

摘　　要：讨论了Hardy空间H2()上的Toeplitz算子Tφ的亚正规性质。Toeplitz算子Tφ的亚正规性质完全由符号函数φ所确定。文章在Toeplitz算子Tφ的亚正规性的一个等价命题(性质1)的基础上,进一步给出了Toeplitz算子Tφ的亚正规性的一个关于符号函数系数的判别法。即Toeplitz算子Tφ的亚正规性等价于一个关于符号函数φ系数的实对称矩阵的半正定性。This paper concerns the hyponormality of Toeplitz operator Tφ, on the Hardy space H2 (NFDA2) of the unit circle NFDA2 in the complex plane, with the symbol φ∈L∈L∞ (NFDA2). The hyponormality of a Toeplitz operator Tφ is determined by the symbol φ. An equivalent theorem about the hyponormality of Toeplitz operator Tφ had been given by C. C. Cowen in . In this paper, authors obtained a judgement method of hyponormality of Toeplitz operator Tφ by the symbol of φ. The hyponormality of Toeplitz operator Tφ is equivalent to the semipositive definite form of a real symmetric matrix about the coefficents of φ.

关 键 词：TOEPLITZ算子 亚正规性 判别法 HARDY空间 符号函数 等价 矩阵 半正定性 

分 类 号：O17[理学—数学]