Mappings that preserve pairs of operators with zero triple Jordan product

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• 作者：M. Dobovi&#x161 ; ek ; B. Kuzma ; G. Le&#x161 ; njak ; C.K. Li ; T. Petek
• 关键词：Matrix algebra ; Jordan triple product ; Nonlinear preserver
• 刊名：Linear Algebra and its Applications
• 出版年：2007
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：15 October 2007
• 卷：426
• 期：2-3
• 页码：255-279
• 文件大小：301 K

摘要

Let ref="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml1&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=9363b6cb3170cee515304f3f2f59dba0">rc="http://www.sciencedirect.com/cache/MiamiImageURL/B6V0R-4NM509R-1-2/0?wchp=dGLbVzW-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=11 width=10> be a field and ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml2&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=372f8bc4392a0e5c32f265117d6e4479" title="Click to view the MathML source">nrc="http://www.sciencedirect.com/scidirimg/entities/2a7e.gif" alt="greater-or-equal, slanted" border=0>3. Suppose ref="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml3&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=52989a2d1a65f28c80022e8bb715b60b">rc="http://www.sciencedirect.com/cache/MiamiImageURL/B6V0R-4NM509R-1-4/0?wchp=dGLbVzW-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=17 width=110> contain all rank-one idempotents. The structure of surjections ref="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml4&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=6547a5f869f547777a29b19a46628e15">rc="http://www.sciencedirect.com/cache/MiamiImageURL/B6V0R-4NM509R-1-5/0?wchp=dGLbVzW-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=16 width=89> satisfying ration:none; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml5&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=da9f9703333d88c55f28d56cd90e8a17" title="Click to view the MathML source">ABA=0rc="http://www.sciencedirect.com/scidirimg/entities/21d4.gif" alt="left right double arrow" border=0>rc="http://www.sciencedirect.com/scidirimg/entities/3d5.gif" alt="phi" border=0>(A)rc="http://www.sciencedirect.com/scidirimg/entities/3d5.gif" alt="phi" border=0>(B)rc="http://www.sciencedirect.com/scidirimg/entities/3d5.gif" alt="phi" border=0>(A)=0 is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space ref="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml6&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=c9add9c47b937a15b4f45414e93b4311">rc="http://www.sciencedirect.com/cache/MiamiImageURL/B6V0R-4NM509R-1-7/0?wchp=dGLbVzW-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=13 width=13>, (b) the space of Hermitian matrices acting on n-dimensional vectors over a skew-field ref="/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4NM509R-1&_mathId=mml7&_user=10&_cdi=5653&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=46d6f57911128860fcb62d2fd91c4a3d">rc="http://www.sciencedirect.com/cache/MiamiImageURL/B6V0R-4NM509R-1-8/0?wchp=dGLbVzW-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=12 width=13>, (c) subsets of self-adjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings rc="http://www.sciencedirect.com/scidirimg/entities/3d5.gif" alt="phi" border=0> on matrices or operators such that