Norms of basic elementary operators on algebras of regular operators

A. W.  Wickstead

doi:10.1090/proc/12664

Norms of basic elementary operators on algebras of regular operators

A. W. Wickstead

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3 Citations (Scopus)

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Abstract

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r_|_|B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.

Original language	English
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Early online date	22 May 2015
DOIs	https://doi.org/10.1090/proc/12664
Publication status	Published - 2015

Keywords

Regular operators, basic elementary operators, Banach lattices

ASJC Scopus subject areas

General Mathematics

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10.1090/proc/12664

Norms of basic elementary operators on algebras of regular operators
© 2015 AMS This is an open access article published under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited. First published in the Proceedings of the American Mathematical Society, 2015, published by the American Mathematical Society.
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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.",

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AB - 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.

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SN - 0002-9939

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Norms of basic elementary operators on algebras of regular operators

Abstract

Keywords

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