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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 7 - Sayı: 2

Operatörlerin Pozitif Lineer Dönüşümleri için Bazı Eşitsizlikler

Some Inequalities for Positive Linear Maps of Operators

İbrahim Halil GÜMÜŞ
Xiaohui FU
Pages
133–140
Publication Date
2022-10-12
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Drawing inspiration from Lin [3], we generalize some operator inequalities due toMond et al. [1] as follows: Let A be positive operator on a Hilbert space with0< . mAM   Then for 2< < p  and every normalized positive linear map  ,  ( ) . 4 ( ) 222 22 pp ppp AM mM m A    Let A be positive operator on a Hilbert space with 0< . mAM   Then for1 <   p and every normalized positive linear map  ,2 2 22 2 1 () ( ) () 4( ) 4( )pp ppM m A Mm AMm M m                  .

📌 3 Key Takeaways

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Objective & Hypothesis:Drawing inspiration from Lin [3], we generalize some operator inequalities due toMond et al. [1] as follows: Let A be positive operator on a Hilbert space with0< . mAM   Then for 2< < p  and every normalized positive linear map  ,  ( ) . 4 ( ) 222 22 pp ppp AM mM m A    Let A be positive operator on a Hilbert space with 0< . mAM   Then for1 <   p and every normalized positive linear map  ,2 2 22 2 1 () ( ) () 4( ) 4( )pp ppM m A Mm AMm M m                  .
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Key Findings & Data:Drawing inspiration from Lin [3], we generalize some operator inequalities due toMond et al. [1] as follows: Let A be positive operator on a Hilbert space with0< . mAM   Then for 2< < p  and every normalized positive linear map  ,  ( ) . 4 ( ) 222 22 pp ppp AM mM m A    Let A be positive operator on a Hilbert space with 0< . mAM   Then for1 <   p and every normalized positive linear map  ,2 2 22 2 1 () ( ) () 4( ) 4( )pp ppM m A Mm AMm M m                  .
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Conclusion & Impact:Drawing inspiration from Lin [3], we generalize some operator inequalities due toMond et al. [1] as follows: Let A be positive operator on a Hilbert space with0< . mAM   Then for 2< < p  and every normalized positive linear map  ,  ( ) . 4 ( ) 222 22 pp ppp AM mM m A    Let A be positive operator on a Hilbert space with 0< . mAM   Then for1 <   p and every normalized positive linear map  ,2 2 22 2 1 () ( ) () 4( ) 4( )pp ppM m A Mm AMm M m                  .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Drawing inspiration from Lin [3], we generalize some operator inequalities due toMond et al. [1] as follows: Let A be positive operator on a Hilbert space with0< . mAM   Then for 2< < p  and every normalized positive linear map  ,  ( ) . 4 ( ) 222 22 pp ppp AM mM m A    Let A be positive operator on a Hilbert space with 0< . mAM   Then for1 <   p and every normalized positive linear map  ,2 2 22 2 1 () ( ) () 4( ) 4( )pp ppM m A Mm AMm M m                  .

Özet

Lin'in [3] teki çalışmasından ilham alarak, Mond ve Pecaric'in [1] deki çalışmasında verilen bazı operatör eşitsizliklerinin genelleştirilmesi şu şekilde yapıldı: A , Hilbert uzayı üzerinde 0 < mAM ? ? şartını sağlayan bir pozitif operatör olmak üzere, 2 < < p ? ve her normalize edilmiş ? pozitif lineer dönüşümü için ? ? 2 2 2 2 2 ( ) () 4 p p p p p M m A A M m ? ? ? ? ? ?? ? ? ? ? ? eşitsizliği geçerlidir. Yine A , Hilbert uzayı üzerinde 0 < mAM ? ? şartını sağlayan bir pozitif operatör olmak üzere, 1 < ? p ? ve her normalize edilmiş ? pozitif lineer dönüşümü için 2 2 2 2 2 1 () ( ) () 4( ) 4( ) p p p p M m A Mm A Mm M m ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? eşitsizliği geçerlidir.

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Cite This Article

GÜMÜŞ, İ. H., FU, X. (2022). Operatörlerin Pozitif Lineer Dönüşümleri için Bazı Eşitsizlikler. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 7 - Sayı: 2, 133–140. https://ajindex.com/articles/428516

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