Geodesic
On totally smooth subspaces of Banach spaces: the Vlasov theorem revisited
Eve Oja1 ; Märt Põldvere2 ; Tauri Viil2
1 Institute of Mathematics and Statistics University of Tartu J. Liivi 2 50409 Tartu, Estonia and Estonian Academy of Sciences Kohtu 6 10130 Tallinn, Estonia
2 Institute of Mathematics and Statistics University of Tartu J. Liivi 2 50409 Tartu, Estonia
Studia Mathematica, Tome 238 (2017) no. 1, pp. 91-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $X$ be a Banach space and let $Y$ be a closed subspace of $X$. We establish new geometric characterizations for $Y$ to be totally smooth in $X$, meaning that every closed subspace of $Y$ has Phelps’ property $U$ in $X$. In particular, this gives a new self-contained proof for a recent theorem of Liao and Wong, and an improved proof for a theorem of Vlasov.
DOI : 10.4064/sm8623-12-2016
Keywords: banach space closed subspace establish geometric characterizations totally smooth meaning every closed subspace has phelps property particular gives self contained proof recent theorem liao wong improved proof theorem vlasov

Eve Oja 1 ; Märt Põldvere 2 ; Tauri Viil 2

1 Institute of Mathematics and Statistics University of Tartu J. Liivi 2 50409 Tartu, Estonia and Estonian Academy of Sciences Kohtu 6 10130 Tallinn, Estonia
2 Institute of Mathematics and Statistics University of Tartu J. Liivi 2 50409 Tartu, Estonia 
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     title = {On totally smooth subspaces of {Banach} spaces: the {Vlasov} theorem revisited},
     journal = {Studia Mathematica},
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Eve Oja; Märt Põldvere; Tauri Viil. On totally smooth subspaces of Banach spaces: the Vlasov theorem revisited. Studia Mathematica, Tome 238 (2017) no. 1, pp. 91-99. doi: 10.4064/sm8623-12-2016

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