Banach lattice

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


  • 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.

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