Γ-supercyclicity

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• 作者：S. Charpentier^a ; ^{stephane.charpentier.1@univ-amu.fr" class="auth_mail" title="E-mail the corresponding author} ; R. Ernst^b ; ^{ernst.r@math.cnrs.fr" class="auth_mail" title="E-mail the corresponding author} ; Q. Menet^c ; ^{quentin.menet@univ-artois.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：47A16
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：270
• 期：12
• 页码：4443-4465
• 全文大小：462 K

文摘

We characterize the subsets Γ of formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si1.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=937c890b688bb983b5aaf45446207765" title="Click to view the MathML source">Cflow="scroll">C for which the notion of Γ-supercyclicity coincides with the notion of hypercyclicity, where an operator T on a Banach space X   is said to be Γ-supercyclic if there exists formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si19.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=400cc67d0a641b7e7a3cbd6030cc494b" title="Click to view the MathML source">x∈Xflow="scroll">x∈X such that f&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=d29c591eb784975e461b5fcd15672bb4">f" data-inlimgeid="1-s2.0-S0022123616001038-si3.gif">flow="scroll">Orb‾false">(Γx,Tfalse">)=X. In addition we characterize the sets formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si131.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=18b1616f4350f480bf321a4a1b4945b0" title="Click to view the MathML source">Γ⊂Cflow="scroll">Γ⊂C for which, for every operator T on X, T   is hypercyclic if and only if there exists a vector formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si19.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=400cc67d0a641b7e7a3cbd6030cc494b" title="Click to view the MathML source">x∈Xflow="scroll">x∈X such that the set formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si5.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=245a5d5705e2bf483541276c29324a5c" title="Click to view the MathML source">Orb(Γx,T)flow="scroll">Orbfalse">(Γx,Tfalse">) is somewhere dense in X  . This extends results by León–Müller and Bourdon–Feldman respectively. We are also interested in the description of those sets formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022123616001038&_mathId=si131.gif&_user=111111111&_pii=S0022123616001038&_rdoc=1&_issn=00221236&md5=18b1616f4350f480bf321a4a1b4945b0" title="Click to view the MathML source">Γ⊂Cflow="scroll">Γ⊂C for which Γ-supercyclicity is equivalent to supercyclicity.