In mathematics, specifically in functional analysis and order theory, a Banach lattice is a Riesz space with a norm such that is a Banach space and for all the implication holds, where as usual .
Examples and constructions
- , together with its absolute value as a norm, is a Banach lattice.
- Let be a topological space, a Banach lattice and the space of bounded, continuous functions from to with norm . becomes a Banach lattice with the pointwise order .
- Abramovich, Yuri A.; Aliprantis, C. D. (2002). An Invitation to Operator Theory. Graduate Studies in Mathematics. 50. American Mathematical Society. ISBN 0-8218-2146-6.