A note on <inline-formula><graphic file="1029-242X-2002-268130-i1.gif"/></inline-formula>-hyponormal operators

• Main Authors: Huruya Tadasi, Kim Young Ok, Ch&#333; Muneo
• Format: Article
• Language: English
• Published: SpringerOpen 2002-01-01
• Series: Journal of Inequalities and Applications
• Subjects: <it>w</it>-hyponormal operator; <it>p</it>-hyponormal operator; Furuta inequality
• Online Access: http://www.journalofinequalitiesandapplications.com/content/7/268130
• ISSN: 1025-5834; 1029-242X

<p/> <p>Let <inline-formula><graphic file="1029-242X-2002-268130-i2.gif"/></inline-formula> be a <inline-formula><graphic file="1029-242X-2002-268130-i3.gif"/></inline-formula>-hyponormal operator with the polar decomposition <inline-formula><graphic file="1029-242X-2002-268130-i4.gif"/></inline-formula>. In this paper, we show the following: (1) If <inline-formula><graphic file="1029-242X-2002-268130-i5.gif"/></inline-formula> is normal, then <inline-formula><graphic file="1029-242X-2002-268130-i6.gif"/></inline-formula> is normal. (2) If <inline-formula><graphic file="1029-242X-2002-268130-i7.gif"/></inline-formula>, then <inline-formula><graphic file="1029-242X-2002-268130-i8.gif"/></inline-formula> is also <inline-formula><graphic file="1029-242X-2002-268130-i9.gif"/></inline-formula>-hyponormal. (3) There exists a <inline-formula><graphic file="1029-242X-2002-268130-i10.gif"/></inline-formula>-hyponormal operator <inline-formula><graphic file="1029-242X-2002-268130-i11.gif"/></inline-formula> such that <inline-formula><graphic file="1029-242X-2002-268130-i12.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-268130-i13.gif"/></inline-formula>.</p>