Inequalities for the normalized determinant of positive operators in Hilbert spaces via some inequalities in terms of Kantorovich ratio [PDF]
Mathematica MoravicaFor positive invertible operators A on a Hilbert space H and a fixed unit vector x ∈ H, define the normalized determinant by ∆x(A) := exp <ln Ax, x>. In this paper we prove among others that, if 0 < mI ≤ A ≤ MI, then 1 ≤ K M m [1/2 - 1/M-m <|A-1/2 (m+M)I|x,x>] ≤ ∆x(A)/ m /M-<Ax,x> M-m M/ <Ax,x>-m M-m ≤ K M /m [1/2 + 1 M-m <
Sever Silvestru
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Improvements of some operator inequalities involving positive linear maps via the Kantorovich constant [PDF]
, 2018 We present some operator inequalities for positive linear maps that generalize and improve the derived results in some recent years. For instant, if $A$ and $B$ are positive operators and $m,m^{'},M,M^{'}$ are positive real numbers satisfying either one of the condition ...
Leila Nasiri, Mojtaba Bakherad
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On an operator Kantorovich inequality for positive linear maps
Journal of Mathematical Analysis and Applications, 2013 We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with ...
Minghua Lin
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New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces
Linear Algebra and its Applications, 2008 If the selfadjoint operator \(A\) on a Hilbert space \(H\) is such that \(mI\leq A\leq MI\), where \(0< m< M\), then the Kantorovich inequality says that \(1\leq\langle Ax, x\rangle\langle A^{-1} x,x\rangle\leq (m+ M)^2/(4mM)\) for any unit vector \(x\) in \(H\).
Sever S Dragomir
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An extension of Kantorovich inequality to n-operators via the geometric mean by Ando–Li–Mathias
Linear Algebra and its Applications, 2006 Let \(A_1,A_2,\dots, A_n\) be positive invertible Hilbert space operators satisfying \(0< mI\leq A_j\leq MI\) for some positive bounds \(0< m< M\). Let also \(G(A_1,A_2,\dots, A_n)\) be the recently defined geometric mean for these operators [see \textit{T.\,Ando}, \textit{C.\,K.\thinspace Li} and \textit{R.\,Mathias} [Linear Algebra Appl.\ 385, 305 ...
Takeaki Yamazaki
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Linear Algebra and its Applications, 2005 Let \(A\) and \(B\) be two strictly positive Hilbert space operators and let \(0< p\leq 1\). Recently, \textit{S.~Furuichi}, \textit{K.~Yanagi} and \textit{K.~Kuriyama} [J.\ Math.\ Phys.\ 45, No.~12, 4868--4877 (2004; Zbl 1064.82001); Linear Algebra Appl.\ 394, 109--118 (2005; Zbl 1059.47018); Linear Algebra Appl.\ 407, 19--31 (2005; Zbl 1071.47021 ...
Takayuki Furuta
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Integral inequalities of Kantorovich and Fiedler types for Hadamard products of operators [PDF]
Mathematical Inequalities & Applications, 2016 Pattrawut Chansangiam
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New versions of refinements and reverses of Young-type inequalities with the Kantorovich constant
Special Matrices, 2023 Recently, some Young-type inequalities have been promoted. The purpose of this article is to give further refinements and reverses to them with Kantorovich constants.
Rashid Mohammad H. M., Bani-Ahmad Feras
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An extension of the operator Kantorovich inequality
Tbilisi Mathematical Journal, 2020 Let \(A\) be a positive invertible operator on a Hilbert space \(H\) such that \(mI\le A\le MI\) where \(I\) is the identity operator on \(H\) and \(m,M\) are positive real numbers. The celebrated Kantorovich inequality asserts that \[ \langle Ax,x\rangle \langle A^{-1}x,x\rangle \le \frac{(m+M)^2}{4mM} \] for all unit vectors \(x\in H\).
Khatib, Yaser +2 more
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Improvements of operator reverse AM-GM inequality involving positive linear maps
Journal of Inequalities and Applications, 2020 In this paper, we shall present some reverse arithmetic-geometric mean operator inequalities for unital positive linear maps. These inequalities improve some corresponding results due to Xue (J. Inequal. Appl. 2017:283, 2017).
Shazia Karim +2 more
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