Spectral inequalities for Kubo-Ando operator means

Lemos, R.; Soares, G.

doi:10.1016/j.laa.2020.08.002

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…This section deals with some results related to Conjecture 1.1. In particular, we shall present a new proof of a refinement of inequality (1) proved by R. Lemos and G. Soares [12, Corollary 7.2] (it worth mentioning here that Corollary 7.2 in [12] deals with a more general result).…”

Section: Results Concerning Conjecture 12mentioning

confidence: 99%

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

Ghabries¹,

Abbas²,

Mourad³

et al. 2021

Preprint

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The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by R. Lemos and G. Soares in [11]. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by R. Bhatia, Y. Lim and T. Yamazaki in [4], and recently proved by T.H. Dinh, R. Dumitru and J.A. Franco in [5] for the Schatten p-norm with 1 ≤ p ≤ ∞.

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Section: Results Concerning Conjecture 12mentioning

confidence: 99%

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

Ghabries¹,

Abbas²,

Mourad³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…If ∼ is deleted and D = I n , then (9.2) was previously given by Ando [4, Theorem 2] and, in this case, the remaining inequalities were obtained by Hiai and Lin [48]. The complete version in Theorem 9.4 is derived in [65]. The inequalities in (9.2) hold for A, B > 0, k = 1, .…”

Section: Ando and Visick's Inequalities For The Hadamard Productmentioning

confidence: 87%

“…If the nonzero operator connections σ, τ, ρ satisfy f 2 σ ≥ f τ f ρ , then (8.1) holds with each connection replaced by its dual [65].…”

Section: Inequalities For Operator Connectionsmentioning

confidence: 99%

Log-majorization Type Inequalities

Bebiano

Lemos

Soares

2022

Trends in Mathematics

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Several inequalities have been established in the context of Hilbert spaces operators or operators algebras. Our discussion will be limited to matrices. Important inequalities in mathematics and other sciences, such as Golden-Thompson inequality or von Neumann trace inequality, and extensions, are revisited. Our main goal is to emphasize the link between majorization theory and other relevant inequalities.

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