Results 151 to 160 of about 349,949 (184)

Operator Inequalities Reverse to the Jensen Inequality

Mathematical Notes, 2001
The paper obtains reverse operator inequalities of Jensen's one as follows: Suppose that \(H\) is a Hilbert space, \(A_{i}=A_{i}^{*}\in B(H)\), \(1\leq i\leq n\), and \(aI\leq A_{i}\leq bI\) for \(i\in\{1,\cdots, n\}\). Further, suppose that \(R_{i}\in B(H)\) are arbitrary operators satisfying the condition \(\sum_{i=1}^{n} R_{i}^{*}R_{i}=I\). If \(f\)
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Inequalities for operators

2009
The purpose of this chapter is to present a series of the local and global estimates for some operators, including the homotopy operator T, the Laplace–Beltrami operator Δ = d d * + d * d, Green’s operator G, the gradient operator ∇, the Hardy–Littlewood maximal operator, and the differential operator, which act on the space of harmonic forms defined ...
Ravi P. Agarwal, Shusen Ding, Craig Nolder   +2 more
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Reverses of Operator Féjer's Inequalities

Tokyo Journal of Mathematics, 2021
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Norm Inequalities for Positive Operators

Letters in Mathematical Physics, 1998
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Bhatia, Rajendra, Kittaneh, Fuad
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CLARKSON INEQUALITIES WITH SEVERAL OPERATORS

Bulletin of the London Mathematical Society, 2004
The authors discuss four norm inequalities. These inequalities hold for the Schatten \(p\)-norm as well as symmetric or unitarily invariant norms, and are extensions of the classical inequalities of \textit{J. A. Clarkson} for the Lebesgue spaces \(L_{p}\) [Trans. Am. Math. Soc. 40, 396--414 (1936; Zbl 0015.35604)].
Bhatia, Rajendra, Kittaneh, Fuad
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Convexity Inequalities for Positive Operators

Positivity, 2006
A (Jensen-type) pointwise convexity inequality of the form \(F (Tf) \leq T [F (f)]\) is proved for a convex function defined on a convex subset of some Banach space \(X\), where \(T\) is the \(X\)-valued extension of a positive operator on some function space.
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Some Norm Inequalities for Operators

Canadian Mathematical Bulletin, 1999
AbstractLet Ai , Bi and Xi (i = 1, 2,…,n) be operators on a separable Hilbert space. It is shown that if f and g are nonnegative continuous functions on [0, ∞) which satisfy the relation f(t)g(t) = t for all t in [0, ∞), thenfor every r > 0 and for every unitarily invariant norm. This result improves some known Cauchy-Schwarz type inequalities. Norm
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Operator Inequalities.

Mathematics of Computation, 1981
Howard A. Levine, Johann Schroder
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Levinson's operator inequality

2014
We give Levinson's operator inequality for unital fields of positive linear mappings and the largest class of continuous functions. Order among quasi- arithmetic means is similarly considered.
Mićić Hot, Jadranka, Praljak, Marjan, Pečarić, Josip   +2 more
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Operator Inequalities Associated with Jensen’s Inequality

2000
We give a survey of various operator inequalities associated with Jensen’s inequality and study the class of operator convex functions of several variables. Related questions are considered.
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