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

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• 作者：Debmalya Sain p>saindebmalya@gmail.com" class="auth_mail" title="E-mail the corresponding authorp>
• 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 pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306606&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306606&_rdoc=1&_issn=0022247X&md5=acb904dabde9d2443bfce2bc2c3c2bf3" title="Click to view the MathML source">Xpan>pan class="mathContainer hidden">pan class="mathCode">$\mathbb{X}$pan>pan>pan>. We also explore the left symmetry of Birkhoff–James orthogonality of linear operators defined on pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306606&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306606&_rdoc=1&_issn=0022247X&md5=acb904dabde9d2443bfce2bc2c3c2bf3" title="Click to view the MathML source">Xpan>pan class="mathContainer hidden">pan class="mathCode">$\mathbb{X}$pan>pan>pan>. Using some of the related results proved in this paper, we finally prove that pan id="mmlsi166" class="mathmlsrc">pii=S0022247X16306606&_rdoc=1&_issn=0022247X&md5=da689d4ee9ae2c0c2fba6db7d4bc0910">pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306606-si166.gif">pt>p://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16306606-si166.gif">pt>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan> (pan id="mmlsi181" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306606&_mathId=si181.gif&_user=111111111&_pii=S0022247X16306606&_rdoc=1&_issn=0022247X&md5=9278175937c1985b570c7cf70d6ad2eb" title="Click to view the MathML source">p≥2,p≠∞pan>pan class="mathContainer hidden">pan class="mathCode">$\mathrm{<font\; color="red">p</font>}\ge 2,\mathrm{<font\; color="red">p</font>}\ne \infty$pan>pan>pan>) is left symmetric with respect to Birkhoff–James orthogonality if and only if T is the zero operator.