Amenable Operators of the Form Normal Plus Compact

作者：Shi, Luo Yi^*; Wu, Yu Jing

来源：Integral Equations and Operator Theory, 2014, 78(1): 79-89.

DOI：10.1007/s00020-013-2115-8

• HILBERT-SPACES

An open question, raised independently by several authors, asks if a closed amenable subalgebra of must be similar to an C (*)-algebra. Recently, Choi, Farah and Ozawa have found a counter-example to this question, but their example is neither separable nor commutative, which leaves the question open for singly-generated algebras. In this paper we continue this line of investigation for special singly-generated algebras. It is shown that if an amenable operator T = N + K, where N is a normal operator, K is a compact operator and sigma (e) (N) has only finite accumulation points, then T is similar to a normal operator; if an amenable operator T = N + K, where N is a normal operator, for some p > 1 and is included in a smooth Jordan curve, then T is similar to a normal operator; if an amenable operator T = N + Q, where N is a normal operator, Q is a polynomial compact operator and NQ = QN, then T is similar to a normal operator; if there exists p, 1 < p < a, such that an amenable operator T satisfies one of the following conditions, then T is similar to a normal operator: (i) ; (ii) ; (iii). I - T*T is an element of C-p.

• 出版日期2014-1
• 单位天津市职业大学; 天津工业大学