Some operator inequalities involving operator means and positive linear maps

2017 ◽  
Vol 66 (6) ◽  
pp. 1186-1198 ◽  
Author(s):  
Maryam Khosravi ◽  
Mohammad Sal Moslehian ◽  
Alemeh Sheikhhosseini
Keyword(s):  
Operator Inequalities ◽  
Linear Maps ◽  
Operator Means ◽  
Positive Linear Maps

scholarly journals Some operator inequalities for operator means and positive linear maps

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3751-3758
Author(s):  
Jianguo Zhao
Keyword(s):  
Type Inequality ◽  
Real Numbers ◽  
Positive Real ◽  
Operator Inequalities ◽  
Linear Map ◽  
Operator Mean ◽  
Linear Maps ◽  
Operator Means ◽  
Arbitrary Operator ◽  
Positive Linear Maps

In this note, some operator inequalities for operator means and positive linear maps are investigated. The conclusion based on operator means is presented as follows: Let ? : B(H) ? B(K) be a strictly positive unital linear map and h-1 IH ? A ? h1IH and h-12 IH ? B ? h2IH for positive real numbers h1, h2 ? 1. Then for p > 0 and an arbitrary operator mean ?, (?(A)??(B))p ? ?p?p(A?*B), where ?p = max {?2(h1,h2)/4)p, 1/16?2p(h1,h2)}, ?(h1h2) = (h1 + h-1 1)?(h2 + h-12). Likewise, a p-th (p ? 2) power of the Diaz-Metcalf type inequality is also established.

Operator Inequalities for Positive Linear Maps

2021 ◽  
pp. 61-87
Author(s):  
Mohammad Bagher Ghaemi ◽  
Nahid Gharakhanlu ◽  
Themistocles M. Rassias ◽  
Reza Saadati
Keyword(s):  
Operator Inequalities ◽  
Linear Maps ◽  
Positive Linear Maps

scholarly journals Improving some operator inequalities for positive linear maps

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4333-4340 ◽  
Author(s):  
Chaojun Yang ◽  
Fangyan Lu
Keyword(s):  
Operator Inequalities ◽  
Linear Map ◽  
Linear Maps ◽  
Operator Version ◽  
Positive Linear Maps

Let 0 < mI ? A ? m'I ? M'I ? B ? MI and p ? 1. Then for every positive unital linear map ?, ?2p(A?tB)?(K(h,2)/41p-1(1+Q(t)(log M'm')2) 2p?2p(A#tB) and ?2p(A?tB)?(K(h,2)/41p-1(1+Q(t)(logM'm')2) 2p(?(A)#t ?(B))2p, where t ? [0,1], h = M/m, K(h,2) = (h+1)2/4h, Q(t) = t2/2(1-t/t)2t and Q(0) = Q(1) = 0. Moreover, we give an improvement for the operator version ofWielandt inequality.

scholarly journals A general double inequality related to operator means and positive linear maps

2012 ◽  
Vol 437 (3) ◽  
pp. 1016-1024
Author(s):  
Rupinderjit Kaur ◽  
Mandeep Singh ◽  
Jaspal Singh Aujla ◽  
M.S. Moslehian
Keyword(s):  
Double Inequality ◽  
Linear Maps ◽  
Operator Means ◽  
Positive Linear Maps
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