Geodesic
Two stars theorems for traces of the Zygmund space
Algebra i analiz, Tome 34 (2022) no. 1, pp. 35-60

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For a Banach space $X$ defined in terms of a big-$O$ condition and its subspace $x$ defined by the corresponding little-$o$ condition, the biduality property (generalizing the concept of reflexivity) asserts that the bidual of $x$ is naturally isometrically isomorphic to $X$. The property is known for pairs of many classical function spaces (such as $(\ell_\infty, c_0)$, $(\mathrm{BMO}, \mathrm{VMO})$, $(\mathrm{Lip}, \mathrm{lip})$, etc.) and plays an important role in the study of their geometric structure. The present paper is devoted to the biduality property for traces to closed subsets $S\subset\mathbb{R}^n$ of a generalized Zygmund space $Z^\omega(\mathbb{R}^n)$. The method of the proof is based on a careful analysis of the structure of geometric preduals of the trace spaces along with a powerful finiteness theorem for the trace spaces $Z^\omega(\mathbb{R}^n)|_S$.
Keywords: Zygmund space, biduality property, trace space, predual space, weak$^*$ topology, finiteness property. 
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     title = {Two stars theorems for traces of the {Zygmund} space},
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A. Brudnyi. Two stars theorems for traces of the Zygmund space. Algebra i analiz, Tome 34 (2022) no. 1, pp. 35-60. http://geodesic.mathdoc.fr/item/AA_2022_34_1_a1/

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