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 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.

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.

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 matrix power and Karcher means inequalities involving positive linear maps

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2625-2634
Author(s):  
Monire Hajmohamadi ◽  
Rahmatollah Lashkaripour ◽  
Mojtaba Bakherad
Keyword(s):  
Weight Vector ◽  
Positive Definite ◽  
Matrix Inequalities ◽  
Positive Definite Matrices ◽  
Linear Map ◽  
Linear Maps ◽  
Karcher Mean ◽  
The Matrix ◽  
Positive Linear Maps ◽  
Matrix Power

In this paper, we generalize some matrix inequalities involving the matrix power means and Karcher mean of positive definite matrices. Among other inequalities, it is shown that if A = (A1,...,An) is an n-tuple of positive definite matrices such that 0 < m ? Ai ? M (i = 1,...,n) for some scalars m < M and ? = (w1,...,wn) is a weight vector with wi ? 0 and ?n,i=1 wi=1, then ?p (?n,i=1 wiAi)? ?p?p(Pt(?,A)) and ?p (?n,i=1 wiAi) ? ?p?p(?(?,A)), where p > 0,? = max {(M+m)2/4Mm,(M+m)2/42p Mm}, ? is a positive unital linear map and t ? [-1,1]\{0}.

scholarly journals Inequalities for sector matrices and positive linear maps

2019 ◽  
Vol 35 ◽  
pp. 418-423 ◽  
Author(s):  
Fuping Tan ◽  
Huimin Che
Keyword(s):  
Geometric Mean ◽  
Positive Definite ◽  
Norm Inequalities ◽  
Linear Map ◽  
Linear Maps ◽  
Positive Linear Map ◽  
Positive Linear Maps

Ando proved that if A, B are positive definite, then for any positive linear map Φ, it holds Φ(A#λB) ≤ Φ(A)#λΦ(B), where A#λB, 0 ≤ λ ≤ 1, means the weighted geometric mean of A, B. Using the recently defined geometric mean for accretive matrices, Ando’s result is extended to sector matrices. Some norm inequalities are considered as well.    

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 Positive linear maps on normal matrices

2018 ◽  
Vol 29 (12) ◽  
pp. 1850088 ◽  
Author(s):  
Jean-Christophe Bourin ◽  
Eun-Young Lee
Keyword(s):  
Normal Matrix ◽  
Linear Combinations ◽  
Linear Map ◽  
Normal Matrices ◽  
Schur Product ◽  
Linear Maps ◽  
Positive Linear Map ◽  
Matrix Formula ◽  
Positive Linear Maps ◽  
Unitary Orbit

For a positive linear map [Formula: see text] and a normal matrix [Formula: see text], we show that [Formula: see text] is bounded by some simple linear combinations in the unitary orbit of [Formula: see text]. Several elegant sharp inequalities are derived, for instance for the Schur product of two normal matrices [Formula: see text], [Formula: see text] for some unitary [Formula: see text], where the constant [Formula: see text] is optimal.

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