Weak-local triple derivations on C<sup>⁎</sup>-algebras and JB<sup>⁎</sup>-triples

Weak-local triple derivations on C^⁎-algebras and JB^⁎-triples

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作者：Marí ; a J. Burgos^a ; ^{maria.burgos@uca.es" class="auth_mail" title="E-mail the corresponding author} ; Juan Carlos Cabello^b ; ^{jcabello@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; Antonio M. Peralta^b ; ^{aperalta@ugr.es" class="auth_mail" title="E-mail the corresponding author}
关键词：47B47 ; 46L57 ; 17C65 ; 47C15 ; 46L05 ; 46L08
刊名：Linear Algebra and its Applications
出版年：2016
出版时间：1 October 2016
年：2016
卷：506
期：Complete
页码：614-627
全文大小：363 K

文摘

We prove that every weak-local triple derivation on a JB^⁎-triple E (i.e. a linear map g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si1.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=dfb7ce5fadc328005460aa0cfce03492" title="Click to view the MathML source">T:E→E

g="si1.

gif" overflow="scroll">T:E→E such that for each g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si2.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=01269196d6e672d35ca5f3ec578b8cee" title="Click to view the MathML source">ϕ∈E^⁎

g="si2.

gif" overflow="scroll">ϕ∈E⁎ and each g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si3.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=b1c145d1acd5a2c867f564526e1a9577" title="Click to view the MathML source">a∈E

g="si3.

gif" overflow="scroll">a∈E, there exists a triple derivation g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si31.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=d10c7d4db73df78fbff1d0c9930f4784" title="Click to view the MathML source">δ_a,ϕ:E→E

g="si31.

gif" overflow="scroll">δa,ϕ:E→E, depending on ϕ and a , such that g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si32.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=3e854ccab70ffe0204410df00aeaf8c4" title="Click to view the MathML source">ϕT(a)=ϕδ_a,ϕ(a)

g="si32.

gif" overflow="scroll">ϕT(a)=ϕδa,ϕ(a)) is a (continuous) triple derivation. We also prove that conditions

g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si215.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=293289b01105690af7ea5c26aaba242c" title="Click to view the MathML source">(h1) $g="si215.$ gif" overflow="scroll">(h1): g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si160.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=871b589b0775dd811da5e67e2017ac05" title="Click to view the MathML source">{a,T(b),c}=0 $g="si160.$ gif" overflow="scroll">{a,T(b),c}=0 for every a, b, c in E with g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si161.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=5c0d932493427fd0627c5302290f6b77" title="Click to view the MathML source">a,c⊥b $g="si161.$ gif" overflow="scroll">a,c⊥b;
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si216.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=39f1e430ea01cb78b771d5477b95e345" title="Click to view the MathML source">(h2) $g="si216.$ gif" overflow="scroll">(h2): g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si10.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=bd3da37fd7ba67b8c9f1db81c13ac7c5" title="Click to view the MathML source">P₂(e)T(a)=−Q(e)T(a) $g="si10.$ gif" overflow="scroll">P2(e)T(a)=−Q(e)T(a) for every norm-one element a in E, and every tripotent e in g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si11.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=a761bfda8229255e4f741f051e9a692b" title="Click to view the MathML source">E^⁎⁎ $g="si11.$ gif" overflow="scroll">E⁎⁎ such that g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si12.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=ed7f2ea08035b60401da32441066c04a" title="Click to view the MathML source">e≤s(a) $g="si12.$ gif" overflow="scroll">e≤s(a) in g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si13.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=45bb1ceee9b3114914bc21a981916ab2">g class="imgLazyJSB inlineImage" height="16" width="48" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516302592-si13.gif"> $g="si13.$ gif" overflow="scroll">E2⁎⁎(e), where g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si14.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=204e447122a1e613ed2dbc12f56276e5" title="Click to view the MathML source">s(a) $g="si14.$ gif" overflow="scroll">s(a) is the support tripotent of a in g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516302592&_mathId=si11.gif&_user=111111111&_pii=S0024379516302592&_rdoc=1&_issn=00243795&md5=a761bfda8229255e4f741f051e9a692b" title="Click to view the MathML source">E^⁎⁎ $g="si11.$ gif" overflow="scroll">E⁎⁎,

are necessary and sufficient to show that a linear map T on a JB^⁎-triple E is a triple derivation.

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