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 i1" class="mathmlsrc">i1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) be the algebra of all bounded linear operators on a complex Banach space X. We describe surjective linear maps ϕ   on i1" class="mathmlsrc">i1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) that satisfy<div class="formula" id="fm0010"><div class="mathml">r_ϕ(T)(x)=0⟹r_T(x)=0${\mathrm{r}}_{\varphi (T)}(x)=0⟹{\mathrm{r}}_T(x)=0$div>div> for every i141" class="mathmlsrc">i141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and T∈L(X)$T\in \mathcal{L}(X)$. We also describe surjective linear maps ϕ   on i1" class="mathmlsrc">i1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) that satisfy<div class="formula" id="fm0020"><div class="mathml">r_T(x)=0⟹r_ϕ(T)(x)=0${\mathrm{r}}_T(x)=0⟹{\mathrm{r}}_{\varphi (T)}(x)=0$div>div> for every i141" class="mathmlsrc">i141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and T∈L(X)$T\in \mathcal{L}(X)$. Furthermore, we characterize maps ϕ   (not necessarily linear nor surjective) on i1" class="mathmlsrc">i1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) which satisfy<div class="formula" id="fm0030"><div class="mathml">${\mathrm{r}}_{\varphi (T)-\varphi (S)}(x)=0\text{if and only if}{\mathrm{r}}_{T-S}(x)=0$div>div> for every i141" class="mathmlsrc">i141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and i148" class="mathmlsrc">i148.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=af4fa2de0891bade88db17bf407ac2ea" title="Click to view the MathML source">T,S∈L(X).