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This article is cited in 43 scientific papers (total in 43 papers)
Singular symmetric functionals and Banach limits with additional invariance properties
P. G. Dodds, B. de Pagter, A. A. Sedaev, E. M. Semenov, F. A. Sukochev
Abstract:
For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy–Littlewood
semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric
functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences.
Received: 11.10.2002
Citation:
P. G. Dodds, B. De Pagter, A. A. Sedaev, E. M. Semenov, F. A. Sukochev, “Singular symmetric functionals and Banach limits with additional invariance properties”, Izv. RAN. Ser. Mat., 67:6 (2003), 111–136; Izv. Math., 67:6 (2003), 1187–1212
Linking options:
https://www.mathnet.ru/eng/im461https://doi.org/10.1070/IM2003v067n06ABEH000461 https://www.mathnet.ru/eng/im/v67/i6/p111
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Abstract page: | 708 | Russian version PDF: | 329 | English version PDF: | 22 | References: | 77 | First page: | 1 |
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