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Norm Inequalities for Positive Operators
Letters in Mathematical Physics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bhatia, Rajendra, Kittaneh, Fuad
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CLARKSON INEQUALITIES WITH SEVERAL OPERATORS
Bulletin of the London Mathematical Society, 2004The 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, 2006A (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, 1999AbstractLet 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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Levinson's operator inequality
2014We 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 +2 more
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Operator Inequalities Associated with Jensen’s Inequality
2000We 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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