Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces
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- 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 n id="mmlsi1" class="mathmlsrc">n 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">X n>n class="mathContainer hidden">n class="mathCode"> n> n> n>. We also explore the left symmetry of Birkhoff–James orthogonality of linear operators defined on n id="mmlsi1" class="mathmlsrc">n 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">X n>n class="mathContainer hidden">n class="mathCode"> n> n> n>. Using some of the related results proved in this paper, we finally prove that n id="mmlsi166" class="mathmlsrc">nce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306606&_mathId=si166.gif&_user=111111111&_pii=S0022247X16306606&_rdoc=1&_issn=0022247X&md5=da689d4ee9ae2c0c2fba6db7d4bc0910">![]()
nlineImage" 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"><noscript>![]()
n:bottom" width="68" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022247X16306606-si166.gif">noscript>n class="mathContainer hidden">n class="mathCode"> n> n> n> (n id="mmlsi181" class="mathmlsrc">n 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≠∞ n>n class="mathContainer hidden">n class="mathCode"> n> n> n>) is left symmetric with respect to Birkhoff–James orthogonality if and only if T is the zero operator.