Norms of basic elementary operators on algebras of regular operators

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Abstract

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ Lr(E) and MA,B is the operator on Lr(E) defined by MA,B(T) = AT B then ||MA,B||r = ||A||r||B||r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.
Original languageEnglish
Number of pages6
JournalProceedings of the American Mathematical Society
Early online date22 May 2015
DOIs
Publication statusPublished - 2015

Keywords

  • Regular operators, basic elementary operators, Banach lattices

ASJC Scopus subject areas

  • Mathematics(all)

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