false
articles
2018-08-01
2019-04-10T14:15
1-8
en
research_article
On Symmetric Spaces With Convergence in Measure on Reflexive Subspaces
A closed subspace H of a symmetric space X on [0, 1] is said to be strongly embedded in X if in H the convergence in X-norm is equivalent to the convergence in 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 analogue of the classical Dunfordâ€“Pettis theorem on relatively weakly compact subsets in L1. At the same time the converse assertion fails for a broad class of separableMarcinkiewicz spaces.
https://scigraph.springernature.com/explorer/license/
http://link.springer.com/10.3103%2FS1066369X18080017
2018-08
Samara State Aerospace University
Samara National Research University, Moskovskoe sh. 34, 443086, Samara, Russia
62
readcube_id
416e4817fe929162406e66933df25c6d817fd7e9f376cb9f1555583fe7557fd7
10.3103/s1066369x18080017
doi
Strakhov
S. I.
Pure Mathematics
8
Mathematical Sciences
dimensions_id
pub.1105773438
S. V.
Astashkin
Russian Mathematics
0021-3446
1934-810X
Springer Nature - SN SciGraph project