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On $ℓ_{q}$ -strictly singular operators on variable exponent spaces

Carlos Buelga; Francisco L. Hernandez — 2015

Commentationes Mathematicae

Strictly singular operators on variable exponent (or Nakano) function spaces $L^{p (\cdot)}$ are characterized in terms of being $ℓ_{q}$ -strictly singular for the values $q$ in the essential range $R_{p (\cdot)}$ of the exponent function. This extends a result of L. Weiss [On perturbations of Fredholm operators in $L_{p}$ -spaces, Proc. Amer. Math. Soc. 67 (1977), 287-292] for $L^{p}$ -spaces.

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On ℓ q -strictly singular operators on variable exponent spaces

On $ℓ_{q}$ -strictly singular operators on variable exponent spaces