Unbounded convergences in vector lattices

• Author / Creator

  Taylor, Mitchell A.

• Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every $u \in X+$. In the literature the unbounded versions of the norm, order and absolute weak convergence have been studied. Here we create a general theory of unbounded convergence, but with a focus on $uo$-convergence and those convergences deriving from locally solid topologies. We also give characterizations of minimal topologies in terms of unbounded topologies and $uo$-convergence. At the end we touch on the theory of bibases in Banach lattices.

• Subjects / Keywords

  • bibasis
  • Schauder basis
  • uo-convergence
  • Banach space
  • minimal topology
  • unbounded topology
  • vector lattice

• Graduation date

  Spring 2019

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-vq30-xr62

• License

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