• Title, Summary, Keyword: operator Inequality

Search Result 84, Processing Time 0.026 seconds

ON CHAOTIC OPERATOR ORDER $A\;{\gg}\;C\;{\gg}\;B$ IN HILBERT SPACES

  • Lin, C.S.
    • East Asian mathematical journal
    • /
    • v.24 no.1
    • /
    • pp.67-79
    • /
    • 2008
  • In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

  • PDF

SOME OPERATOR INEQUALITIES INVOLVING IMPROVED YOUNG AND HEINZ INEQUALITIES

  • Moazzen, Alireza
    • The Pure and Applied Mathematics
    • /
    • v.25 no.1
    • /
    • pp.39-48
    • /
    • 2018
  • In this work, by applying the binomial expansion, some refinements of the Young and Heinz inequalities are proved. As an application, a determinant inequality for positive definite matrices is obtained. Also, some operator inequalities around the Young's inequality for semidefinite invertible matrices are proved.

THE FEKETE-SZEGÖ INEQUALITY FOR CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY CONVOLUTION BETWEEN GENERALIZED AL-OBOUDI DIFFERENTIAL OPERATOR AND SRIVASTAVA-ATTIYA INTEGRAL OPERATOR

  • Challab, K.A.;Darus, M.;Ghanim, F.
    • Korean Journal of Mathematics
    • /
    • v.26 no.2
    • /
    • pp.191-214
    • /
    • 2018
  • The aim of this paper is to investigate the Fekete $Szeg{\ddot{o}}$ inequality for subclass of analytic functions defined by convolution between generalized Al-Oboudi differential operator and Srivastava-Attiya integral operator. Further, application to fractional derivatives are also given.

A NOTE ON THE GENERALIZED VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

  • Kum, Sangho
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.3
    • /
    • pp.319-324
    • /
    • 2009
  • In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

  • PDF

Operator Inequalities Related to Angular Distances

  • Taba, Davood Afkhami;Dehghan, Hossein
    • Kyungpook Mathematical Journal
    • /
    • v.57 no.4
    • /
    • pp.623-630
    • /
    • 2017
  • For any nonzero elements x, y in a normed space X, the angular and skew-angular distance is respectively defined by ${\alpha}[x,y]={\parallel}{\frac{x}{{\parallel}x{\parallel}}}-{\frac{y}{{\parallel}y{\parallel}}}{\parallel}$ and ${\beta}[x,y]={\parallel}{\frac{x}{{\parallel}y{\parallel}}}-{\frac{y}{{\parallel}x{\parallel}}}{\parallel}$. Also inequality ${\alpha}{\leq}{\beta}$ characterizes inner product spaces. Operator version of ${\alpha}$ has been studied by $ Pe{\check{c}}ari{\acute{c}}$, $ Raji{\acute{c}}$, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of ${\beta}$ by using Douglas' lemma. We also prove that the operator version of inequality ${\alpha}{\leq}{\beta}$ holds for commutating normal operators. Some examples are presented to show essentiality of these conditions.

The Hilbert-Type Integral Inequality with the System Kernel of-λ Degree Homogeneous Form

  • Xie, Zitian;Zeng, Zheng
    • Kyungpook Mathematical Journal
    • /
    • v.50 no.2
    • /
    • pp.297-306
    • /
    • 2010
  • In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.