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Absolute norms on vector lattices

Borwein, Jonathan M. and Yost, D. A. (1984) Absolute norms on vector lattices. Proc. Edinburgh Math. Soc., 27 . pp. 215-222.

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Abstract

Recall that a norm ‖.‖ on a vector lattice E is absolute if ‖∣x∣‖=‖x‖ for all x∉E; and monotone if ‖x‖≤‖y‖ whenever 0≤x≤y. If the norm is both absolute and monotone, it is called a Riesz norm. It is easy to show that a norm is Riesz if and only if ‖x‖≤‖y‖ whenever ∣x∣≤∣y∣. A Banach lattice is a vector lattice equipped with a complete Riesz norm.

Item Type: Article
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 21 Feb 2015 10:34
Last Modified: 21 Feb 2015 10:34
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1624

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