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On algebraic properties of sets of Banach ideal function spaces

Eugene Tokarev
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Abstract

It is shown that every set I(m) of Banach lattices of measurable functions defined on a measure space (Q,S,m), equipped with a some natural ordering became a modular lattice, which is Dedekind complete provided m is a probability measure. Moreover, some natural operations on considered spaces are in Galois connexion.

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Eugene Tokarev. 2002-11-12. On algebraic properties of sets of Banach ideal function spaces. https://arxiv.org/abs/math/0209322

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