Real Analysis Exchange

Strictly Singular Operators on Banach Lattices

Francisco L. Hernández and Evgeny M. Semenov

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Abstract

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

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

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.rae/1561622430

Digital Object Identifier
doi:10.14321/realanalexch.44.1.0037

Mathematical Reviews number (MathSciNet)
MR3951332

Zentralblatt MATH identifier
07088961

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

Keywords
Strictly singular operators Rearrangement invariant function spaces Disjointly strictly singular operators

Citation

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. https://projecteuclid.org/euclid.rae/1561622430


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