Further refinements of Young’s type inequality for positive linear maps

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
Mohamed Amine Ighachane ◽  
Mohamed Akkouchi
Keyword(s):  
Type Inequality ◽  
Linear Maps ◽  
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.

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 .

scholarly journals Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 313-324
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Positive Operators ◽  
Selfadjoint Operators ◽  
Popoviciu’S Inequality ◽  
Linear Maps ◽  
Superquadratic Functions ◽  
Operator Version ◽  
Positive Linear Maps

AbstractIn this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

scholarly journals All 2-positive linear maps from M3(C) to M3(C) are decomposable

2016 ◽  
Vol 503 ◽  
pp. 233-247 ◽  
Author(s):  
Yu Yang ◽  
Denny H. Leung ◽  
Wai-Shing Tang
Keyword(s):  
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
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