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Uniform λ-property in L1∩L∞

Bohonos A., Płuciennik R.

Commentationes Mathematicae

2015

Vol 55, No. 2

171--181

Here it is proved that the space L1∩L∞ equipped with the standard interpolation norm ∥⋅∥L1∩L∞=max{∥⋅∥L1,∥⋅∥L∞} has the uniform λ-property if and only if μ(T)≤1. Replacing the standard norm with an equivalent one ∥⋅∥′L1∩L∞= ∥⋅∥L1+∥⋅∥L∞, a different result is obtained.: (L1∩L∞,∥⋅∥′L1∩L∞) has the uniform λ-property if and only if \(\mu (T)

Orlicz-Bochner sequence spaces that have the uniform λ-property

Shi Z., Zhang P.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr spec.

215-227

Necessary and sufficient conditions in order that Orlicz-Bochner sequence spaces equipped with Luxemburg norm have the uniform [lambda] property are given.