- Title
- Absolute norms on vector lattices
- Creator
- Borwein, J. M.; Yost, D. T.
- Relation
- Proceedings of the Edinburgh Mathematical Society Vol. 27, Issue 2, p. 215-222
- Relation
- http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=3076132&fulltextType=RA&fileId=S0013091500022318
- Publisher
- Edinburgh Mathematical Society
- Resource Type
- journal article
- Date
- 1984
- Description
- 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.
- Subject
- norms; Riesz norms; vector; lattice
- Identifier
- http://hdl.handle.net/1959.13/940973
- Identifier
- uon:13142
- Identifier
- ISSN:0013-0915
- Language
- eng
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