Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras
We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we of...
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| Vydáno v: | Linear algebra and its applications Ročník 510; s. 329 - 345 |
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| Jazyk: | angličtina |
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01.12.2016
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| ISSN: | 0024-3795, 1873-1856 |
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| Abstract | We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we offer some applications to the measure algebra M(G) and the generalized Fourier algebra Ap(G) of a locally compact group G. |
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| AbstractList | We study a finite dimensional invariant subspace property similar to Fan's Theorem on semigroups for arbitrary Banach algebras A in terms of amenability of X(A,ϕ), the closed subalgebra of A generated by the set of all maximal elements in A with respect to a character ϕ. As a consequence, we offer some applications to the measure algebra M(G) and the generalized Fourier algebra Ap(G) of a locally compact group G. |
| Author | Nasr-Isfahani, Rasoul Nemati, Mehdi Shahmoradi, Somayeh |
| Author_xml | – sequence: 1 givenname: Rasoul surname: Nasr-Isfahani fullname: Nasr-Isfahani, Rasoul email: isfahani@cc.iut.ac.ir organization: Department of Mathematical Sciences, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran – sequence: 2 givenname: Mehdi surname: Nemati fullname: Nemati, Mehdi email: m.nemati@cc.iut.ac.ir organization: Department of Mathematical Sciences, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran – sequence: 3 givenname: Somayeh surname: Shahmoradi fullname: Shahmoradi, Somayeh email: shahmoradi@math.iut.ac.ir organization: Department of Mathematical Sciences, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran |
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| Cites_doi | 10.4153/CMB-2012-015-3 10.1017/S0305004108001126 10.4064/sm202-3-1 10.1016/0022-247X(83)90203-2 10.5802/aif.1197 10.1090/tran/6442 10.1017/S0013091500004673 10.1093/qmath/hat015 10.1215/ijm/1256052955 10.1112/S0024610702003381 10.1016/S0022-1236(02)00040-X 10.4064/sm-129-3-207-223 10.1016/j.jfa.2012.07.013 10.1017/S0305004107000874 10.1016/j.aim.2011.12.022 10.4064/cm-51-1-195-205 10.4064/fm-118-3-161-175 10.1016/j.jmaa.2008.03.037 10.4064/cm132-2-2 10.1016/S1385-7258(65)50047-0 |
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| Keywords | 15A30 43A15 Banach algebra 43A20 Maximal element 43A10 Fixed point property Locally compact group 43A07 46H05 Finite dimensional invariant subspace Character amenable |
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| References | Lau, Paterson, Wong (br0160) 1989; 32 Lau, Zhang (br0180) 2012; 263 Dashti, Nasr-Isfahani, Soltani (br0020) 2014; 57 Nasr-Isfahani, Nemati (br0250) 2013; 132 Monfared (br0220) 2003; 198 Lau (br0130) 1983; 97 Lau, Ludwig (br0150) 2012; 229 Lau, Zhang (br0170) 2016; 368 Monfared (br0210) 2008; 144 Desaulniers, Nasr-Isfahani, Nemati (br0030) 2011; 402 Hewitt, Ross (br0050) 1970 Lau (br0140) 1987; 51 Lust-Piquard (br0190) 1989; 39 Kaniuth, Lau, Pym (br0110) 2008; 344 Mitchell (br0200) 1970; 14 Dales, Ghahramani, Helemdkii (br0010) 2002; 66 Kaniuth, Lau, Pym (br0100) 2008; 144 Fan (br0040) 1965; 27 Iohvidov (br0070) 1949; 21 Naimark (br0230) 1963; 24 Naimark (br0240) 1963; 4 Iohvidov, Krein (br0080) 1960; 13 Lau (br0120) 1983; 118 Nasr-Isfahani, Soltani Renani (br0260) 2011; 202 Hu (br0060) 1998; 129 Nasr-Isfahani, Soltani Renani (br0270) 2014; 65 Pontrjagin (br0290) 1944; 8 Pier (br0280) 1988; vol. 172 Krein (br0090) 1955; 1 Lau (10.1016/j.laa.2016.08.028_br0130) 1983; 97 Naimark (10.1016/j.laa.2016.08.028_br0230) 1963; 24 Monfared (10.1016/j.laa.2016.08.028_br0220) 2003; 198 Lau (10.1016/j.laa.2016.08.028_br0150) 2012; 229 Krein (10.1016/j.laa.2016.08.028_br0090) 1955; 1 Monfared (10.1016/j.laa.2016.08.028_br0210) 2008; 144 Dashti (10.1016/j.laa.2016.08.028_br0020) 2014; 57 Kaniuth (10.1016/j.laa.2016.08.028_br0100) 2008; 144 Kaniuth (10.1016/j.laa.2016.08.028_br0110) 2008; 344 Lau (10.1016/j.laa.2016.08.028_br0170) 2016; 368 Hu (10.1016/j.laa.2016.08.028_br0060) 1998; 129 Iohvidov (10.1016/j.laa.2016.08.028_br0070) 1949; 21 Nasr-Isfahani (10.1016/j.laa.2016.08.028_br0270) 2014; 65 Lust-Piquard (10.1016/j.laa.2016.08.028_br0190) 1989; 39 Fan (10.1016/j.laa.2016.08.028_br0040) 1965; 27 Desaulniers (10.1016/j.laa.2016.08.028_br0030) 2011; 402 Iohvidov (10.1016/j.laa.2016.08.028_br0080) 1960; 13 Lau (10.1016/j.laa.2016.08.028_br0180) 2012; 263 Pontrjagin (10.1016/j.laa.2016.08.028_br0290) 1944; 8 Naimark (10.1016/j.laa.2016.08.028_br0240) 1963; 4 Dales (10.1016/j.laa.2016.08.028_br0010) 2002; 66 Pier (10.1016/j.laa.2016.08.028_br0280) 1988; vol. 172 Lau (10.1016/j.laa.2016.08.028_br0120) 1983; 118 Lau (10.1016/j.laa.2016.08.028_br0160) 1989; 32 Mitchell (10.1016/j.laa.2016.08.028_br0200) 1970; 14 Nasr-Isfahani (10.1016/j.laa.2016.08.028_br0250) 2013; 132 Lau (10.1016/j.laa.2016.08.028_br0140) 1987; 51 Nasr-Isfahani (10.1016/j.laa.2016.08.028_br0260) 2011; 202 Hewitt (10.1016/j.laa.2016.08.028_br0050) 1970 |
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| SubjectTerms | Banach algebra Character amenable Finite dimensional invariant subspace Fixed point property Locally compact group Maximal element |
| Title | Finite dimensional invariant subspaces for algebras of linear operators and amenable Banach algebras |
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