Results 31 to 40 of about 597 (98)
Jensen's inequality for spectral order and submajorization [PDF]
, 2007 Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f (φ{symbol} (a))
Antezana, Jorge Abel +2 more
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Concave functions of partitioned matrices with numerical ranges in a sector
, 2017 We prove two inequalities for concave functions and partitioned matrices whose numerical ranges in a sector. These complement some results of Zhang in [Linear Multilinear Algebra 63 (2015) 2511–2517].
L. Hou, D. Zhang
semanticscholar +1 more source
Extensions of Three Matrix Inequalities to Semisimple Lie Groups
Special Matrices, 2014 We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context ofsemisimple Lie groups.
Liu Xuhua, Tam Tin-Yau
doaj +1 more source
, 2013 Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval [0, 1].
Drnovšek, Roman
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Some inequalities involving positive linear maps under certain conditions
Operators and Matrices, 2019 We demonstrate that several well-known classical inequalities also hold for some positive linear maps on matrix algebra. It is shown that for such maps the Jensen inequality hold for all ordinary convex functions. Mathematics subject classification (2010)
R. Kumar, Rajesh Sharma, I. Spitkovsky
semanticscholar +1 more source
Mathematical Inequalities & Applications, 2019 For positive real numbers a and b , the weighted power mean Pt,q(a,b) and the weighted Heron mean Kt,q(a,b) are defined as follows: For t ∈ [0,1] and q ∈ R , Pt,q(a,b) = {(1− t)aq + tbq} q and Kt,q(a,b) = (1− q)a1−tbt + q{(1− t)a+ tb} .
Masatoshi Ito
semanticscholar +1 more source
Refined Young inequalities with Specht's ratio
, 2011 In this paper, we show that the $\nu$-weighted arithmetic mean is greater than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\nu$-weighted geometric mean is greater than the product of the ...
Furuichi, Shigeru
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On some classical trace inequalities and a new Hilbert-Schmidt norm inequality
, 2018 Let A be a positive semidefinite matrix and B be a Hermitian matrix. Using some classical trace inequalities, we prove, among other inequalities, that ∥ ∥AsB+BA1−s ∥ ∥ 2 ∥ ∥AtB+BA1−t ∥ ∥ 2 for 2 s t 1 . We conjecture that this inequality is also true for
M. Hayajneh, Saja Hayajneh, F. Kittaneh
semanticscholar +1 more source
Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector
, 2013 Let $A = \pmatrix A_{11} & A_{12} \cr A_{21} & A_{22}\cr\pmatrix \in M_n$, where $A_{11} \in M_m$ with $m \le n/2$, be such that the numerical range of $A$ lies in the set $\{e^{i\varphi} z \in \IC: |\Im z| \le (\Re z) \tan \alpha\}$, for some $\varphi ...
Li, Chi-Kwong, Sze, Nung-Sing
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Inequalities for numerical invariants of sets of matrices [PDF]
Linear Algebra and its Applications, 368 (2003), 71-81., 2002 We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger and Wang as an immediate corollary.
arxiv +1 more source