- Examples and constructions
- See also
- References
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 
.
See also
- Banach space
- Riesz space
- Lattice (order)
References
- {{cite book
| last = Abramovich
| first = Yuri A.
| author2 = Aliprantis, C. D.
| year = 2002
| title = An Invitation to Operator Theory
| series= Graduate Studies in Mathematics
| volume= 50
| publisher = American Mathematical Society
| location =
| isbn = 0-8218-2146-6
}}{{Functional Analysis}}{{mathanalysis-stub}}
2 : Functional analysis|Order theory
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