The Fuglede-Putnam theorem for <inline-formula><graphic file="1029-242X-2006-47481-i1.gif"/></inline-formula>-quasihyponormal operators

• Main Author: Kim In Hyoun
• Format: Article
• Language: English
• Published: SpringerOpen 2006-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2006/47481

<p/> <p>We show that if <inline-formula><graphic file="1029-242X-2006-47481-i2.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2006-47481-i3.gif"/></inline-formula>-quasihyponormal operator and <inline-formula><graphic file="1029-242X-2006-47481-i4.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2006-47481-i5.gif"/></inline-formula>-hyponormal operator, and if <inline-formula><graphic file="1029-242X-2006-47481-i6.gif"/></inline-formula>, where <inline-formula><graphic file="1029-242X-2006-47481-i7.gif"/></inline-formula> is a quasiaffinity (i.e., a one-one map having dense range), then <inline-formula><graphic file="1029-242X-2006-47481-i8.gif"/></inline-formula> is a normal and moreover <inline-formula><graphic file="1029-242X-2006-47481-i9.gif"/></inline-formula> is unitarily equivalent to <inline-formula><graphic file="1029-242X-2006-47481-i10.gif"/></inline-formula>.</p>