On maps preserving operators of local spectral radius zero

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• 作者：M. Elhodaibi^a ; ^{hodaibi2001@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; A. Jaatit^b ; ^{a.jaatit@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 47B49 ; secondary ; 47B48 ; 47A10 ; 47A11
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：512
• 期：Complete
• 页码：191-201
• 全文大小：267 K

文摘

Let lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X)lass="mathContainer hidden">lass="mathCode">g="si1.gif" overflow="scroll">Llse">(Xlse">) be the algebra of all bounded linear operators on a complex Banach space X. We describe surjective linear maps ϕ   on lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X)lass="mathContainer hidden">lass="mathCode">g="si1.gif" overflow="scroll">Llse">(Xlse">) that satisfy for every lsi141" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈Xlass="mathContainer hidden">lass="mathCode">g="si141.gif" overflow="scroll">x∈X and lsi31" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si31.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=38cc490618cfd493b4bd335f84309015" title="Click to view the MathML source">T∈L(X)lass="mathContainer hidden">lass="mathCode">g="si31.gif" overflow="scroll">T∈Llse">(Xlse">). We also describe surjective linear maps ϕ   on lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X)lass="mathContainer hidden">lass="mathCode">g="si1.gif" overflow="scroll">Llse">(Xlse">) that satisfy for every lsi141" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈Xlass="mathContainer hidden">lass="mathCode">g="si141.gif" overflow="scroll">x∈X and lsi31" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si31.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=38cc490618cfd493b4bd335f84309015" title="Click to view the MathML source">T∈L(X)lass="mathContainer hidden">lass="mathCode">g="si31.gif" overflow="scroll">T∈Llse">(Xlse">). Furthermore, we characterize maps ϕ   (not necessarily linear nor surjective) on lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X)lass="mathContainer hidden">lass="mathCode">g="si1.gif" overflow="scroll">Llse">(Xlse">) which satisfy for every lsi141" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈Xlass="mathContainer hidden">lass="mathCode">g="si141.gif" overflow="scroll">x∈X and lsi148" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si148.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=af4fa2de0891bade88db17bf407ac2ea" title="Click to view the MathML source">T,S∈L(X)lass="mathContainer hidden">lass="mathCode">g="si148.gif" overflow="scroll">T,S∈Llse">(Xlse">).