scholarly journals Some Multiplicative Inequalities for Heinz Operator Mean

2021 ◽  
Vol 2 (1) ◽  
pp. 1-10
Author(s):  
Silvestru Sever Dragomir ◽  
Keyword(s):  
Operator Mean

scholarly journals Order of operators determined by operator mean

2015 ◽  
Vol 67 (1) ◽  
pp. 39-50
Author(s):  
Masaru Nagisa ◽  
Mitsuru Uchiyama
Keyword(s):  
Operator Mean

scholarly journals Geometric convexity of an operator mean

Positivity ◽  
2019 ◽  
Vol 24 (3) ◽  
pp. 615-629 ◽  
Author(s):  
Shuhei Wada
Keyword(s):  
Operator Mean

scholarly journals Comparison of operator mean geodesics

2008 ◽  
pp. 287-298
Author(s):  
Jun Ichi Fujii ◽  
Jadranka Mić ć Hot ◽  
Josip Pečarić ◽  
Yuki Seo
Keyword(s):  
Operator Mean

scholarly journals VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS

2020 ◽  
pp. 1-18 ◽  
Author(s):  
MOHSEN KIAN ◽  
MOHAMMAD SAL MOSLEHIAN ◽  
YUKI SEO
Keyword(s):  
Hilbert Space ◽  
Norm Inequality ◽  
Power Mean ◽  
Variable Operator ◽  
Linear Map ◽  
Power Means ◽  
Operator Mean ◽  
Positive Linear Map ◽  
Euclidean Mean

Abstract For an n-tuple of positive invertible operators on a Hilbert space, we present some variants of Ando–Hiai type inequalities for deformed means from an n-variable operator mean by an operator mean, which is related to the information monotonicity of a certain unital positive linear map. As an application, we investigate the monotonicity of the power mean from the deformed mean in terms of the generalized Kantorovich constants under the operator order. Moreover, we improve the norm inequality for the operator power means related to the Log-Euclidean mean in terms of the Specht ratio.

scholarly journals CONVEX MULTIVARIABLE TRACE FUNCTIONS

2002 ◽  
Vol 14 (07n08) ◽  
pp. 631-648 ◽  
Author(s):  
ELLIOTT H. LIEB ◽  
GERT K. PEDERSEN
Keyword(s):  
Convex Function ◽  
Short Proof ◽  
Trace Function ◽  
C Algebra ◽  
Operator Mean ◽  
Lower Semi ◽  
Continuous Trace ◽  
Densely Defined

For any densely defined, lower semi-continuous trace τ on a C*-algebra A with mutually commuting C*-subalgebras A1, A2, … An, and a convex function f of n variables, we give a short proof of the fact that the function (x1, x2, …, xn)→ τ (f (x1, x2, …, xn)) is convex on the space [Formula: see text]. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called ℓ-convexity, show how it applies to traces, and give some examples. In particular we show that the Kadison–Fuglede determinant is concave and that the trace of an operator mean is always dominated by the corresponding mean of the trace values.

scholarly journals Bond-Operator Mean Field Theory for the Bilayer Heisenberg Model

1999 ◽  
Vol 68 (1) ◽  
pp. 247-252 ◽  
Author(s):  
Yasuhiro Matsushita ◽  
Martin P. Gelfand ◽  
Chikara Ishii
Keyword(s):  
Field Theory ◽  
Heisenberg Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Operator Mean

scholarly journals Continued Fraction Expansion of the Heinz Operator Mean

2020 ◽  
Vol 8 (6) ◽  
pp. 311
Author(s):  
Kacem Belhroukia ◽  
Salah Salhi ◽  
Ali Kacha
Keyword(s):  
Continued Fraction ◽  
Continued Fraction Expansion ◽  
Operator Mean
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