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Journal of Inequalities and Applications

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Open Access 01.12.2006 | Research Article

Extensions of the results on powers of -hyponormal and -hyponormal operators

verfasst von: Changsen Yang, Jiangtao Yuan

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

Firstly, we will show the following extension of the results on powers of

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq3_HTML.gif

-hyponormal and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq4_HTML.gif

-hyponormal operators: let

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq5_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq6_HTML.gif

be positive integers, if

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq7_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq8_HTML.gif

-hyponormal for

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq9_HTML.gif

, then: (i) in case

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq10_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq11_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq12_HTML.gif

hold, (ii) in case

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq13_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq14_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq15_HTML.gif

hold. Secondly, we will show an estimation on powers of

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq16_HTML.gif

-hyponormal operators for

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq17_HTML.gif

which implies the best possibility of our results. Lastly, we will show a parallel estimation on powers of

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq18_HTML.gif

-hyponormal operators as follows: let

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq19_HTML.gif

, then the following hold for each positive integer

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq20_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq21_HTML.gif

: (i) there exists a log-hyponormal operator

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq22_HTML.gif

such that

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq23_HTML.gif

, (ii) there exists a

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq24_HTML.gif

-hyponormal operator

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq25_HTML.gif

such that

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F36919/MediaObjects/13660_2004_Article_1588_IEq26_HTML.gif

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Titel: Extensions of the results on powers of -hyponormal and -hyponormal operators
verfasst von: Changsen Yang
Jiangtao Yuan
Publikationsdatum: 01.12.2006
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/36919

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