Generalized matrix version of reverse Hölder inequality

Kaur, Rupinderjit; Singh, Mandeep; Aujla, Jaspal Singh

doi:10.1016/j.laa.2010.09.027

Cited by 11 publications

(5 citation statements)

References 6 publications

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“…In [13], the authors showed another way to find a reverse Choi-Davis-Jensen inequality. If f is a strictly concave differentiable function on an interval [m, M ] with m < M and Φ is a unital positive linear map, then…”

Section: Some Reverses Of the Bellman Operator Inequalitymentioning

confidence: 99%

Some complements and refinements of the operator Bellman inequality

Liao

Long

Cao³

et al. 2023

Preprint

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We present several generalizations and refinements of the Bellman inequality involving the interpolation paths by the Callebautinequality and apply it to the operator geometric means acting on a Hilbert space. We also give some reverse operator Bellmaninequalities. Finally, we get a reverse Choi-Davis-Jensen inequality concerning operator mean and use it for obtaining agenernalization of the reverse operator Bellman type inequality. AMS Subject Classification: 15A42; 47A63; 47A30

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Section: Some Reverses Of the Bellman Operator Inequalitymentioning

confidence: 99%

Some complements and refinements of the operator Bellman inequality

Liao

Long

Cao³

et al. 2023

Preprint

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show abstract

“…In [8], the authors showed another way to find a reverse Choi-Davis-Jensen inequality. If f is a strictly concave differentiable function on an interval [m, M] with m < M and Φ is a unital positive linear map, then…”

Section: Is a Concave And Operator Monotone Function On [M M]mentioning

confidence: 99%

Some operator Bellman type inequalities

Bakherad

Morassaei

2015

Indagationes Mathematicae

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“…It is also called the generalized perspective function associated to (operator) convex function f (see [9,13,21]). The variants of (14) with operator concave functions f = (·) 1/2 and f = log(·) lead to the notions of geometric mean [16,18] and of relative operator entropy [1,10], respectively. Moreover, sums (integrals) of maps of type (14) give Csiszár operator f -divergence [8,21] (see also (29)).…”

Section: Preliminariesmentioning

confidence: 99%

Shannon like inequalities for f-connections of positive linear maps and positive operators

Niezgoda

2015

Linear Algebra and its Applications

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In this paper, we investigate a map (T, B) → T fT − (B), called an f -connection, induced by an operator convex (concave) function f , where T − denotes a reflexive generalized inverse of a positive linear map T between unital C * -algebras A and B of Hilbert space operators, and B ∈ B. Some special cases of f -connection with invertible T are related to geometric operator mean, relative operator entropy and Csiszár operator f -divergence. We formulate conditions under which the inequality f (1)I ≤ n k=1 T k fT − k (B k ) holds, where T k : A → B are positive linear maps and B k ∈ Ran T k . In particular, the following Shannon like inequality 0 ≤ n k=1 T k fT − k (B k ) is shown for an operator convex function f with f (1) = 0. The obtained results are specified for Csiszár operator f -divergence. Some recent results by Isa et al. (2013) [15] are recovered.

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Generalized matrix version of reverse Hölder inequality

Cited by 11 publications

References 6 publications

Some complements and refinements of the operator Bellman inequality

Some complements and refinements of the operator Bellman inequality

Some operator Bellman type inequalities

Shannon like inequalities for f-connections of positive linear maps and positive operators

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