(1) St-Petersburg Federal Pedagogic University, Mojka 48, St-Petersburg, 191186, Russia;(2) St-Petesburg Federal University of Technology and Design, Bolshaya Morskaya 18, St-Petersburg, 191065, Russia
Abstract:
It is known that the Banach completion Y = bX of a normed lattice X need not preserve the properties to be Dedekind complete or σ-Dedekind complete. In this paper it is proved that the countable
interpolation property and the property to be sequentially order complete are preserved under the Banach completion. To prove
this results we found some sufficient conditions (which are close to necessary ones) on X which secure for Y to have the countable interpolation property and (respectively) to be sequentially order complete. These conditions are obtained
with the help of the newly developed techniques based on representations of normed lattices. It is well known that order continuity,
and σ-order continuity of a norm are preserved under the Banach completion. Here necessary and sufficient conditions on X to secure these properties in Y are discussed.
Mathematics Subject Classification 2000: 46B42, 46E15