Mostrando recursos 1 - 4 de 4

  1. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...
    (application/pdf) - 03-nov-2017

  2. Vector Inequalities For Two Projections in Hilbert Spaces and Applications

    Dragomir, Silvestru Sever
    In this paper we establish some vector inequalities related to Schwarz and Buzano results. We show amongst others that in an inner product space $H$ we have the inequality \begin{equation*} \frac{1}{4}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle -2\left\langle Px,y\right\rangle -2\left\langle Qx,y\right\rangle \right\vert \right] \geq \left\vert \left\langle QPx,y\right\rangle \right\vert \end{equation*} for any vectors $x,y$ and $P,Q$ two orthogonal projections on $H$. If $PQ=0$ we also have \begin{equation*} \frac{1}{2}\left[ \left\Vert x\right\Vert \left\Vert y\right\Vert +\left\vert \left\langle x,y\right\rangle \right\vert \right] \geq \left\vert \left\langle Px,y\right\rangle +\left\langle Qx,y\right\rangle \right\vert \end{equation*} for any $x,y\in H.$ ¶ Applications for norm and numerical radius inequalities of two bounded...
    (application/pdf) - 04-nov-2017

  3. Norm Estimates for Powers of Products of Operators in a Banach Space

    Gil’, Michael
    Let $A$ and $B$ be bounded linear operators in a Banach space. We consider the following problem: if $\Sigma_{k=0}^{\infty} || A^{k} |||| B^{k} || \lt\infty$, under what conditions $\Sigma_{k=0}^{\infty} || (AB)^{k} || \lt \infty$?
    (application/pdf) - 03-nov-2017

  4. Norm Estimates for Powers of Products of Operators in a Banach Space

    Gil’, Michael
    Let $A$ and $B$ be bounded linear operators in a Banach space. We consider the following problem: if $\Sigma_{k=0}^{\infty} || A^{k} |||| B^{k} || \lt\infty$, under what conditions $\Sigma_{k=0}^{\infty} || (AB)^{k} || \lt \infty$?
    (application/pdf) - 04-nov-2017

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