Norm-attaining lattice homomorphisms
نویسندگان
چکیده
In this paper we study the structure of set ${\\rm Hom}(X,\\mathbb{R})$ all lattice homomorphisms from a Banach $X$ into $\\mathbb{R}$. Using relation among and disjoint families, prove that topological dual free FBL}(A)$ generated by $A$ contains family cardinality $2^{|A|}$, answering question B. de Pagter A. W. Wickstead. We also deal with norm-attaining homomorphisms. For classical lattices, as $c_0$, $L_p$- $C(K)$-spaces, every homomorphism on it attains its norm, which shows, in particular, there is no James theorem for class functions. that, indeed, $C(K,X)$ norm whenever has order continuous norm. On other hand, provide what seems to be first example literature does not attain general, existence characterization attaining their lattices. As consequence, shown Bishop–Phelps type holds true setting, i.e., can approximated
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ژورنال
عنوان ژورنال: Revista Matematica Iberoamericana
سال: 2021
ISSN: ['2235-0616', '0213-2230']
DOI: https://doi.org/10.4171/rmi/1292