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SUMMARY:Max Arnott (University of Lancaster)
DTSTART:20201214T150000Z
DTEND:20201214T160000Z
DTSTAMP:20260423T035931Z
UID:GOBA/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/12/">Ke
 rnels of bounded operators on transfinite Banach sequence spaces</a>\nby M
 ax Arnott (University of Lancaster) as part of Groups\, Operators\, and Ba
 nach Algebras Webinar\n\n\nAbstract\nFor a Banach space $E$\, we ask the f
 ollowing question: "Is it true that for every closed subspace $Y$ of $E$\,
  there exists some bounded linear operator $T : E \\to E$ for which $Y= \\
 ker T$?"\n\nIn a recent paper by Niels Laustsen and Jared White\, it was p
 roved that every separable Banach space answers the question in the positi
 ve\, and that there exists a reflexive Banach space which answers the ques
 tion in the negative.\n\nLet $\\Gamma$ be an uncountable cardinal. In this
  talk we will investigate the above question for the transfinite Banach se
 quence spaces $\\ell_p(\\Gamma)$ for $1\\leq p <\\infty$\, and $c_0(\\Gamm
 a)$. The question is answered in the negative for $\\ell_1(\\Gamma)$\, and
  in the positive for $\\ell_p(\\Gamma)$ for $1 < p <\\infty$ and $c_0(\\Ga
 mma)$.\n
LOCATION:https://researchseminars.org/talk/GOBA/12/
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