جستجوی مقالات مرتبط با کلیدواژه « Specht's ratio » در نشریات گروه « ریاضی »

We present some new numerical radius inequalities of Hilbert space operators. We improve and generalize some inequalities with re- spect to Specht’s ratio. Let A and B be two positive invertible operators on a Hilbert space H and let X be a bounded operator on H. Then ω((A♮B)X) ≤ 1 2S(√h) ∥X∗BX + A∥, (h > 0, h ̸ = 1) where ∥ · ∥, ω(·), S(·), and ♮ denote the usual operator norm, numeri- cal radius, the Specht’s ratio, and the operator geometric mean, respec- tively.

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follows that begin{equation*} omega^2(A^*B)leq frac{1}{2S(sqrt{h})}Big||A|^{4}+|B|^{4}Big|-displaystyle{inf_{|x|=1}} frac{1}{4S(sqrt{h})}big(biglangle big(A^*A-B^*Bbig) x,xbigranglebig)^2 end{equation*} for some $h>0$, where $|cdot|,,,,omega(cdot)$ and $S(cdot)$ denote the usual operator norm, numerical radius and the Specht's ratio, respectively.