Maps on the positive definite cone of a C^⁎-algebra preserving certain quasi-entropies

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• 作者：Lajos Molná ; r^a ; ^b ; ¹ ; ^{molnarl@math.u-szeged.hu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Preservers ; Quasi-entropy ; C⁎C⁎-algebra ; Positive definite cone ; Jordan *-isomorphism ; Central element
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：206-221
• 全文大小：384 K

文摘

We describe the structure of those bijective maps on the cone of all positive invertible elements of a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305790&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305790&_rdoc=1&_issn=0022247X&md5=eb3bc8a2de8f03336704de4055419cfd" title="Click to view the MathML source">C^⁎class="mathContainer hidden">class="mathCode">$C^{⁎}$-algebra with a normalized faithful trace which preserve certain kinds of quasi-entropy. It is shown that essentially any such map is equal to a Jordan *-isomorphism of the underlying algebra multiplied by a central positive invertible element.