Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces

详细信息    查看全文

• 作者：Debmalya Sain ^{saindebmalya@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Birkhoff&ndash ; James orthogonality ; Linear operators ; Norm attainment ; Left symmetry of orthogonality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：860-866
• 全文大小：281 K

文摘

In this paper we characterize Birkhoff–James orthogonality of linear operators defined on a finite dimensional real Banach space X$\mathbb{X}$. We also explore the left symmetry of Birkhoff–James orthogonality of linear operators defined on X$\mathbb{X}$. Using some of the related results proved in this paper, we finally prove that lineImage" height="20" width="68" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306606-si166.gif">$T\in \mathbb{L}(l_p^2)$ (p&ge;2,p≠∞$p\&<font\; color="red">ge</font>;2,p\ne \infty$) is left symmetric with respect to Birkhoff–James orthogonality if and only if T is the zero operator.