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Let B (n , q) be the class of block graphs on n vertices having all their blocks of the same size. We prove that if G ∈ B (n , q) has at most three pairwise adjacent cut vertices then the minimum spectral radius ρ (G) is attained at a unique graph. In addition, we present a lower bound for ρ (G) when G ∈ B (n , q). [ABSTRACT FROM AUTHOR]

Let G (n , α) be the class of block graphs on n vertices and prescribed independence number α. In this article we prove that the maximum spectral radius ρ (G) , among all graphs G ∈ G (n , α) , is reached at a unique graph. As a byproduct we obtain an upper for ρ (G) , when G ∈ G (n , α). [ABSTRACT FROM AUTHOR]

In this paper, we obtain some refinements of the known operator inequalities for the p -Schatten class. In addition, we obtain an approach to the inequalities conjectured by Audenaert and Kittaneh for the p -Schatten class. [ABSTRACT FROM AUTHOR]

Abstract: We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach–Porta–Recht inequality. We also characterize the class of operators satisfying under certain conditions. [Copyright &y& Elsevier]

Abstract: In this work we characterize normal invertible operators via inequalities with unitarily invariant norm of elementary operators. [Copyright &y& Elsevier]

Abstract: The aim of this work is to apply the complex interpolation method to norms of -tuples of operators in a symmetrically-normed ideal defined by a symmetric norming function (s.n.f.). The norms considered define Finsler metrics in a certain manifold of positive operators, and can be regarded as weighted -norms, the weight being a positive invertible operator. [Copyright &y& Elsevier]

Abstract: The celebrated Heinz inequality asserts that for , , every unitarily invariant norm and . In this paper, we present several improvement of the Heinz inequality by using the convexity of the function , some integration techniques and various refinements of the Hermite–Hadamard inequality. In the setting of matrices we prove that for real numbers α, β. [Copyright &y& Elsevier]