Bartle-dunford-schwartz integration for positive vector measures and representation of quasi-banach
lattices Articles uri icon

authors

  • SANCHEZ PEREZ, E. A.
  • TRADACETE PEREZ, PEDRO

publication date

  • January 2016

start page

  • 387

end page

  • 402

issue

  • 2

volume

  • 17

International Standard Serial Number (ISSN)

  • 1345-4773

Electronic International Standard Serial Number (EISSN)

  • 1880-5221

abstract

  • An order-based integration of scalar functions with respect to positive vector measures with values in quasi-Banach lattices is presented. It is proved that it coincides with the Bartle-Dunford-Schwartz-type integration for the case of positive measures. These ideas are used to obtain general representation theorems for abstract order continuous quasi-Banach lattices with weak unit without any previous representation of these spaces as spaces of integrable functions. In the case of quasi-Banach lattices having some convexity, it is shown that this representation can be improved.

keywords

  • quasi-banach lattice; vector-valued integration; representation theorem; spaces; operators