Inequalities for J−contractions Involving the Α−power Mean
نویسنده
چکیده
A selfadjoint involutive matrix J endows C with an indefinite inner product [·, ·] given by [x, y] := 〈Jx, y〉, x, y ∈ C. We present some inequalities of indefinite type involving the α−power mean and the chaotic order. These results are in the vein of those obtained by E. Kamei [6, 7].
منابع مشابه
Operator Inequalities for J–contractions
A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] = 〈Jx,y〉 , x,y ∈ Cn. Characterizations of the J -chaotic order Log(A) J Log(B) are presented for J -selfadjoint matrices A,B with positive eigenvalues, in terms of operator functions involving the α -power mean and the J -relative entropy. An indefinite complete form of the Furuta inequality and s...
متن کاملSome weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
متن کاملRICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM
Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...
متن کاملOptimal inequalities for the power, harmonic and logarithmic means
For all $a,b>0$, the following two optimal inequalities are presented: $H^{alpha}(a,b)L^{1-alpha}(a,b)geq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain[frac{1}{4},1)$, and $ H^{alpha}(a,b)L^{1-alpha}(a,b)leq M_{frac{1-4alpha}{3}}(a,b)$ for $alphain(0,frac{3sqrt{5}-5}{40}]$. Here, $H(a,b)$, $L(a,b)$, and $M_p(a,b)$ denote the harmonic, logarithmic, and power means of order $p$ of two positive numbers...
متن کامل(m1,m2)-Convexity and Some New Hermite-Hadamard Type Inequalities
In this manuscript, a new class of extended (m1,m2)-convex and concave functions is introduced. After some properties of (m1,m2)-convex functions have been given, the inequalities obtained with Hölder and Hölder-İşcan and power-mean and improwed power-mean integral inequalities have been compared and it has been shown that the inequality with Hölder-İşcan inequality gives a better approach than...
متن کامل