A version of Kalton’s theorem for the space of regular operators

Xanthos, Foivos

doi:10.1007/s13348-013-0101-8

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The Space Of Regular Bounded Martingales On a Banach Lattice1

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2016

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“…Again, one may expect similarities with the well-known theory of regular operators; see, e.g., [16,17]. It is well known that every regular operator on a Banach lattice is bounded and the space of regular operators on an order complete Banach lattice is a Banach lattice under the regular norm.…”

Section: The Space Of Regular Bounded Martingales On a Banach Latticementioning

confidence: 84%

Spaces of regular abstract martingales

Troitsky

Xanthos

2016

Journal of Mathematical Analysis and Applications

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In [15,10], the authors introduced and studied the space M r of regular martingales on a vector lattice and the space M r of bounded regular martingales on a Banach lattice. In this note, we study these two spaces from the vector lattice point of view. We show, in particular, that these spaces need not be vector lattices. However, if the underlying space is order complete then M r is a vector lattice and M r is a Banach lattice under the regular norm.

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Section: The Space Of Regular Bounded Martingales On a Banach Latticementioning

confidence: 84%