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Journal of Inequalities and Applications

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Open Access 01-12-2006 | Research Article

The Fuglede-Putnam theorem for -quasihyponormal operators

Author: In Hyoun Kim

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

We show that if

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq2_HTML.gif

is a

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq3_HTML.gif

-quasihyponormal operator and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq4_HTML.gif

is a

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq5_HTML.gif

-hyponormal operator, and if

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq6_HTML.gif

, where

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq7_HTML.gif

is a quasiaffinity (i.e., a one-one map having dense range), then

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq8_HTML.gif

is a normal and moreover

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq9_HTML.gif

is unitarily equivalent to

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F47481/MediaObjects/13660_2004_Article_1602_IEq10_HTML.gif

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Title: The Fuglede-Putnam theorem for-quasihyponormal operators
Author: In Hyoun Kim
Publication date: 01-12-2006
Publisher: Springer International Publishing
Published in: Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/47481

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