Results 1 to 10 of about 1,767,691 (332)
Convex multivariate operator means [PDF]
Linear Algebra and its Applications, 2019 The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing a technique to prove the existence of multivariate operator means that are not necessarily monotone.
Hansen, Frank
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Means of unitary operators, revisited [PDF]
MATHEMATICA SCANDINAVICA, 2007 It is proved that an operator with bound not exceeding $(n-2)n^{-1}$ in a $C^*$-algebra is the mean of $n$ unitay operators in that algebra.
Uffe Haagerup +2 more
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Operator means and matrix functions
Linear Algebra and its Applications, 1990 AbstractOperator means are nonlinear matrix functions that arise in the study of interconnection of n-ports (Hilbert ports). We survey some of the relations among operator means, shorted operators, Dini's theorem, and norm convergence. Matrix valued functions are used to present new examples of many diverse convergence behaviors.
William A. Green, T. D. Morley
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Ergodicity in strongly correlated systems [PDF]
Condensed Matter Physics, 2006 We present a concise and systematic, review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green's function formalism by means of the equations of motion approach.
A.Avella, F.Mancini, E.Plekhanov
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The logarithmic mean of two convex functionals [PDF]
Open Mathematics, 2020 The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well.
Raïssouli Mustapha, Furuichi Shigeru
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Classification of operators by means of their operational calculus [PDF]
Transactions of the American Mathematical Society, 1965 Shmuel Kantorovitz
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Criteria for monotonicity of operator means [PDF]
Journal of the Mathematical Society of Japan, 2003 Let {ψr}r>0 and {ϕr}r>0 be the families of operator monotone functions on [0,∞) satisfying ψr(xrg(x))=xr,ϕr(xrg(x))=xrh(x), where g and h are continuous and g is increasing. Suppose σψa and σ∅r are the corresponding operator connections. We will show that if AσψaB≥1(a>0), then ArσψrB and Arσ∅rB are both increasing for r≥a, and then we will apply this ...
Mitsuru Uchiyama
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Geometric convexity of an operator mean [PDF]
arXiv, 2019 Let $\sigma$ be an operator mean in the sense of Kubo and Ando. If the representation function $f$ of $\sigma$ satisfies $f_\sigma (t)^p\le f_\sigma(t^p) \text{ for all } p>1,$ then the operator mean is called a pmi mean. Our main interest is the class of pmi means (denoted by PMI). To study PMI, the operator mean $\sigma$, wherein $$f_\sigma(\sqrt{xy})
arxiv +5 more sources
Certain integral inequalities involving tensor products, positive linear maps, and operator means [PDF]
Journal of Inequalities and Applications, 2016 We present a number of integral inequalities involving tensor products of continuous fields of bounded linear operators, positive linear maps, and operator means.
Pattrawut Chansangiam
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