BISHOP'S PROPERTY (β) AND RIESZ IDEMPOTENT FOR K-QUASI-PARANORMAL OPERATORS
BISHOP'S PROPERTY (β) AND RIESZ IDEMPOTENT FOR K-QUASI-PARANORMAL OPERATORS
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DOI：
10.15352/bjma/1337014673
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发表时间：
2012
影响因子：
1.2
通讯作者：
S. Mécheri
中科院分区：
文献类型：
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作者：
S. Mécheri
对满足毕夏普性质（）的算子的研究是一个非常有趣的问题，目前世界上许多数学家都在研究这个问题。最近内山和田桥（导演）。矩阵4(2009),517-524)证明了超常算子具有Bishop的性质（）。本文引入了一类新的算子，我们称之为k-拟超正规算子。如果一个算子T满足||T k+1 x|| 2 ||T k+2 x|||T k x||，则称其为k-拟超正规算子。这类算子包含了超正规算子类和拟类A算子类。证明了k-拟超常算子的基本性质，给出了k-拟超常算子的结构定理。我们还证明了Bishop的性质（）对这类操作符是成立的。最后，我们证明了如果E对k-拟常算子T谱的非零孤立点0是Riesz幂等的当且仅当t0的零空间ker(t0) ker（t0）是自伴随的。
The study of operators satisfying Bishop's property ( ) is of sig- nificant interest and is currently being done by a number of mathematicians around the world. Recently Uchiyama and Tanahashi (Oper. Matrices 4 (2009), 517-524) showed that a paranormal operator has Bishop's property ( ). In this paper we introduce a new class of operators which we call the class of k- quasi-paranormal operators. An operator T is said to be a k-quasi-paranormal operator if it satisfies ||T k+1 x|| 2 || T k+2 x|||T k x|| for all x 2 H where k is a natural number. This class of operators contains the class of paranormal oper- ators and the class of quasi-class A operators. We prove basic properties and give a structure theorem of k-quasi-paranormal operators. We also show that Bishop's property ( ) holds for this class of operators. Finally, we prove that if E is the Riesz idempotent for a nonzero isolated point 0 of the spectrum of a k-quasi-paranormal operator T, then E is self-adjoint if and only if the null space of T 0, ker(T 0) ker(T 0).