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

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 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 Improved Kantorovich and Wielandt operator inequalities for positive linear maps

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 871-876 ◽  
Author(s):  
Wenshi Liao ◽  
Junliang Wu
Keyword(s):  
Hilbert Space ◽  
Operator Inequalities ◽  
Hilbert Space Operators ◽  
Linear Maps ◽  
Positive Linear Maps

This paper improves and generalizes the Kantorovich and Wielandt inequalities for positive linear maps on Hilbert space operators and presents more general and precise results compared to many recent results.

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.

Positive Linear Maps on C*-Algebras

1972 ◽  
Vol 24 (3) ◽  
pp. 520-529 ◽  
Author(s):  
Man-Duen Choi
Keyword(s):  
Vector Spaces ◽  
Complex Numbers ◽  
Complex Matrices ◽  
Completely Positive ◽  
C Algebras ◽  
Linear Maps ◽  
Positive Linear Maps

The objective of this paper is to give some concrete distinctions between positive linear maps and completely positive linear maps on C*-algebras of operators.Herein, C*-algebras possess an identity and are written in German type . Capital letters A, B, C stand for operators, script letters for vector spaces, small letters x, y, z for vectors. Capital Greek letters Φ, Ψ stand for linear maps on C*-algebras, small Greek letters α, β, γ for complex numbers.We denote by the collection of all n × n complex matrices. () = ⊗ is the C*-algebra of n × n matrices over .

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