Geodesic
On symmetric spaces with convergence in measure on reflexive subspaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 3-11.

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A closed subspace H of a symmetric space X on [0,1] is said to be strongly embedded in X if in H a convergence in X-norm is equivalent to the convergence in Lebesgue measure. We study symmetric spaces X with the property that all their reflexive subspaces are strongly embedded in X. We prove that it is the case for all spaces, which satisfy an analog of the classical Dunford–Pettis theorem of relatively weakly compact subsets in L1. At the same time the converse assertion fails for a wide class of separable Marcinkiewicz spaces.
Mots-clés : symmetric spaces, reflexive subspace, Marcinkiewicz space, equicontinuity of norms. 
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     title = {On symmetric spaces with convergence in measure on reflexive subspaces},
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}
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S. V. Astashkin; S. I. Strakhov. On symmetric spaces with convergence in measure on reflexive subspaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 3-11. https://geodesic-test.mathdoc.fr/item/IVM_2018_8_a0/

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