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Strictly singular embeddings between rearrangement invariant spaces. (English) Zbl 1041.46022

The main result of the present paper, namely: “The canonical embedding of a rearrangement-invariant Banach space \(E\) into \(L_{1}\) is not strictly singular if and only if \(E\supset G\), where \(G\) denotes the closure of \(L_{\infty}\) in the Orlicz space \(L_{M}\), generated by the Orlicz function \(M(u)=\exp\left( u^{2}\right) -1\)” was obtained much earlier by the reviewer; see E. V. Tokarev, Usp. Mat. Nauk 40, 221–222 (1985; Zbl 0589.46021), Theorem 4.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Citations:

Zbl 0589.46021
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