کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896608 | 1630589 | 2018 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A dichotomy property for locally compact groups
ترجمه فارسی عنوان
یک ویژگی دوگانگی برای گروه های جمع و جور محلی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of â1. For that purpose, we transfer to general locally compact groups the notion of interpolation (I0) set, which was defined by Hartman and Ryll-Nardzewsky [24] for locally compact abelian groups. Thus we prove that for every sequence {gn}n<Ï in a locally compact group G, then either {gn}n<Ï has a weak Cauchy subsequence or contains a subsequence that is an I0 set. This result is subsequently applied to obtain sufficient conditions for the existence of Sidon sets in a locally compact group G, an old question that remains open since 1974 (see [31] and [19]). Finally, we show that every locally compact group strongly respects compactness extending thereby a result by Comfort, Trigos-Arrieta, and Wu [13], who established this property for abelian locally compact groups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 275, Issue 4, 15 August 2018, Pages 869-891
Journal: Journal of Functional Analysis - Volume 275, Issue 4, 15 August 2018, Pages 869-891
نویسندگان
MarÃa V. Ferrer, Salvador Hernández, Luis Tárrega,