On the commutants modulo Cp of A2 and A3

Journal of the Australian Mathematical Society

Fuad Kittaneh¹ 

关键词: commutant;    normal operators;    subnormal operators;    isometry;    Schatten p-class;   

DOI  :  10.1017/S1446788700028056

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We prove the following statements about bounded linear operators on a complex separable infinite dimensional Hilbert space. (1) Let A and B* be subnormal operators. If A2X = XB2 and A3X = XB3 for some operator X, then AX = XB. (2) Let A and B* be subnormal operators. If A2X – XB2 ∈ Cp and A3X – XB3 ∈ Cp for some operator X, then AX − XB ∈ C8p. (3) Let T be an operator such that 1 − T*T ∈ Cp for some p ≥1. If T2X − XT2 ∈ Cp and T3X – XT3 ∈ Cp for some operator X, then TX − XT ∈ Cp. (4) Let T be a semi-Fredholm operator with ind T < 0. If T2X − XT2 ∈ C2 and T3X − XT3 ∈ C2 for some operator X, then TX − XT ∈ C2.

【 授权许可】

Unknown