Results 221 to 230 of about 1,391 (258)

Operator Inequalities Involving Operator Monotone Functions

2021
In this chapter, we gather improvements of known operator inequalities involving positive linear maps, geometric means, operator monotone functions, and doubly concave functions. We note that these types of operator inequalities have essential applications in the theory of functional equations in non-euclidean geometry.
Mohammad Bagher Ghaemi, Nahid Gharakhanlu, Themistocles M. Rassias, Reza Saadati   +3 more
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Operator monotone functions on accretive matrices

Positivity, 2023
The authors prove three main results. First, let \(f\) be a real-valued operator monotone function on the positive real line. Let \(A\) be an accretive matrix. An integral representation for \(f(A)\) in terms of a positive measure on the nonnegative real line is obtained. Next, let \(f\) be an operator monotone function from the positive real line into
Ghazanfari, Amir Ghasem, Malekinejad, Somayeh   +1 more
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On some operator monotone functions

Integral Equations and Operator Theory, 2002
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Uchiyama, Mitsuru, Hasumi, Morisuke
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Monotone Operators Representable by l.s.c. Convex Functions

Set-Valued Analysis, 2005
The authors generalize a theorem due to \textit{S. Fitzpatrick} [Proc. Cent. Math. Anal. Aust. Natl. Univ. 20, 59--65 (1988; Zbl 0669.47029)], who gave a representation for maximal monotone operators by convex functions. They obtain several characterizations for monotone operators in Banach spaces through convex lower semicontinuous functions and ...
Martínez-Legaz, J.-E., Svaiter, B. F.
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New inequalities for operator monotone functions

Annals of the University of Craiova - Mathematics and Computer Science Series, 2021
"In this paper we prove that, if f:[0,∞)→R is operator monotone on [0,∞), then for all A, B such that 0<α≤A≤β<γ≤B≤δ for some positive constants α, β, γ, δ, 0≤(γ-β)((f(δ)-f(β))/(δ-β))≤f(B)-f(A)≤(δ-α)((f(γ)-f(α))/(γ-α)). In particular, we have the refinement and reverse of the celebrated Löwner-Heinz inequality 0<(γ-β)((δ^{r}-β^{r})/(δ-β))≤B^{r}-
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Strong monotonicity of operator functions

Integral Equations and Operator Theory, 2000
Let \(A\), \(B\) be bounded selfadjoint operators on a Hilbert space. We will give a formula to get the maximum subspace \({\mathcal M}\) such that \({\mathcal M}\) is invariant for \(A\) and \(B\), and \(A|_{{\mathcal M}}= B|_{{\mathcal M}}\). We will use this to show strong monotonicity or strong convexity of operator functions. We will see that when
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On operator monotone and operator convex functions

Russian Mathematics, 2016
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Correction: New characterizations of operator monotone functions

Acta Scientiarum Mathematicarum
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Vo, Bich Khue, Dinh, Trung Hoa, Osaka, Hiroyuki   +2 more
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Operator Monotone and Operator Convex Functions

1997
In this chapter we study an important and useful class of functions called operator monotone functions. These are real functions whose extensions to Hermitian matrices preserve order. Such functions have several special properties, some of which are studied in this chapter. They are closely related to properties of operator convex functions.
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Maximal Monotone Operators and Saddle Functions I

Zeitschrift für Analysis und ihre Anwendungen, 1986
We investigate the monotone operator T_K \subseteq E \times E^*, f \in T_Kx\colon = [–f, f] \in \partial K(x,x) , which is defined via the subdifferential of a concave-convex saddle function K
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