Acta Mathematica Sinica

, Volume 11, Issue 4, pp 389–398

# Normality preserving multiplication operators

• Lu Shijie
• Lu Fangyan
Article

## Abstract

We show that a multiplication operator Φ(T)=ATB is normality preserving if and only if it is hyponormality preserving, if and only if it is either of the formA=fg,B=hf, orA=D,B=λD* for someλ∈C andD* D=I. Also we show that Φ is (semi-) Fredholmness prserving if and only ifA andB are (semi-) Fredholm operators.

### Keyword

Multiplication operators Normality preserving Fredholmness preserving

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## Copyright information

© Science Press 1995

## Authors and Affiliations

• Lu Shijie
• 1
• Lu Fangyan
• 1
1. 1.Department of MathematicsZhejiang UniversityHangzhouChina