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Completeness and modular cross-symmetry in normed linear spaces. (English) Zbl 0786.46027
\(L_ c(X)\) denotes the lattice of all subspaces of a normed linear space \(X\). Various results are obtained, for example,
Corollary 2.4 (Holland): Let \(X\) be an inner product space and let \(L_ c(X)\) be cross-symmetric. Then \(X\) is a Hilbert space.
46B99 Normed linear spaces and Banach spaces; Banach lattices
06C99 Modular lattices, complemented lattices
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