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On the Representation of Some Subnormal Operators
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作者 席俊 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期36-40,共5页
Let T be pure subnormal operator. In this paper necessary and sufficiert conditions that T=N+K are given,where N is normal, K is quasinormal and NK=KN.
关键词 subnormal operators self-dual subnormal operators
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On quasi-similarity of subnormal operators 被引量:2
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作者 Zhi-jian QIU Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China 《Science China Mathematics》 SCIE 2007年第3期305-312,共8页
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) ... For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 展开更多
关键词 subnormal operator QUASI-SIMILARITY harmonic measure Hardy space 47B20 30H05 30E10 46E15
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Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160 被引量:1
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作者 王公宝 马吉溥 《Northeastern Mathematical Journal》 CSCD 2001年第1期45-48,共4页
In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented a... In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper. 展开更多
关键词 weighted shift near subnormal operator subnormal operator hyponormal operator M P generalized inverse
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