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pro vyhledávání: '"Werner, Dirk"'
Autor:
Werner, Dirk
This note surveys Wolfgang Lusky's proof of uniqueness of the Gurariy spaces and mentions further developments.
Externí odkaz:
http://arxiv.org/abs/2309.06146
Autor:
Werner, Dirk
We revisit some ideas of K.-M.~Perfekt who has provided an elegant framework to detect the biduality between function or sequence spaces defined in terms of some $o$- resp.\ $O$-condition. We present new proofs under somewhat weaker assumptions than
Externí odkaz:
http://arxiv.org/abs/2105.02614
We provide sufficient conditions on a Banach space $X$ in order that there exist norm attaining operators of rank at least two from $X$ into any Banach space of dimension at least two. For example, a rather weak such condition is the existence of a n
Externí odkaz:
http://arxiv.org/abs/1905.08272
We study the problem of totally smooth renormings of Banach spaces and provide such renormings for spaces which are weakly compactly generated. We also consider renormings for $(a,B,c)$-ideals.
Externí odkaz:
http://arxiv.org/abs/1807.07335
We present a construction that enables one to find Banach spaces $X$ whose sets $NA(X)$ of norm attaining functionals do not contain two-dimensional subspaces and such that, consequently, $X$ does not contain proximinal subspaces of finite codimensio
Externí odkaz:
http://arxiv.org/abs/1709.01756
The notion of slicely countably determined (SCD) sets was introduced in 2010 by A.~Avil\'{e}s, V.~Kadets, M.~Mart\'{i}n, J.~Mer\'{i} and V.~Shepelska. We solve in the negative some natural questions about preserving being SCD by the operations of uni
Externí odkaz:
http://arxiv.org/abs/1708.05218
We study when the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon-Nikod\'ym derivatives. We will show that this can sometimes be done, but there are also principal cases in which this cannot be done.
Externí odkaz:
http://arxiv.org/abs/1704.06481
Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analysed. A geometric description is given in terms of nonlinear slices. Some local versions of these prop
Externí odkaz:
http://arxiv.org/abs/1507.04185
Publikováno v:
Proc. Amer. Math. Soc. 143 (2015), 5281-5292
We introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer to the non-linear case some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators.
Externí odkaz:
http://arxiv.org/abs/1407.4018
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