Geodesic
Inductive and projective limits of Banach spaces of measurable functions with order unites with respect to power parameter
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 80-85

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We prove that a measurable function $f$ is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order units $f^\alpha$ and $f^\beta$ with $\alpha>\beta>0$. We show that it is natural to understand the limit of ordered vector spaces with order units $f^\alpha$ ($\alpha$ approaches to infinity) as a direct sum of one inductive and one projective limits. We also obtain some properties for the corresponding limit topologies.
Keywords: inductive limit, projective limit, initial topology, final topology, order unit space, measurable functions, Banach space, locally convex space.
Mots-clés : Fréchet space 
@article{IVM_2016_10_a10,
     author = {A. Novikov and Z. Eskandarian},
     title = {Inductive and projective limits of {Banach} spaces of measurable functions with order unites with respect to power parameter},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--85},
     publisher = {mathdoc},
     number = {10},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_10_a10/}
}
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A. Novikov; Z. Eskandarian. Inductive and projective limits of Banach spaces of measurable functions with order unites with respect to power parameter. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2016), pp. 80-85. http://geodesic.mathdoc.fr/item/IVM_2016_10_a10/