Real Analysis Exchange

Strictly Singular Operators on Banach Lattices

Francisco L. Hernández and Evgeny M. Semenov

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We survey several properties of the class of strictly singular operators defined on Banach lattices of measurable functions and rearrangement invariant function spaces. The related classes of disjointly strictly singular operators and super strictly singular operators are also discussed. In particular we present interpolation properties of strictly singular operators between \(L_p-L_q\) spaces.

Article information

Real Anal. Exchange, Volume 44, Number 1 (2019), 37-48.

First available in Project Euclid: 27 June 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B42: Banach lattices [See also 46A40, 46B40] 47B60: Operators on ordered spaces

Strictly singular operators Rearrangement invariant function spaces Disjointly strictly singular operators


Hernández, Francisco L.; Semenov, Evgeny M. Strictly Singular Operators on Banach Lattices. Real Anal. Exchange 44 (2019), no. 1, 37--48. doi:10.14321/realanalexch.44.1.0037.

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