سامانه اطلاعات پژوهشی


پژوهش های ریاضی، جلد ۵، شماره ۲، صفحات ۲۲۱-۲۲۸


عنوان فارسی	یک توپولوژی موضعاً محدب روی جبرهای بورلینگ

چکیده فارسی مقاله	فرض کنید یک گروه موضعاً فشرده، یک تابع وزن و فضای توابع اندازهپذیر روی باشد که اساساً کراندار و در بینهایت صفر میشوند. در این مقاله توپولوژی موضعاً محدب را روی فضای وزندار بررسی میکنیم. نشان می‌دهیم که دوگان با این توپولوژی برابر فضای باناخ است. علاوه بر این، برخی ویژگی‌های فضای با توپولوژی مذکور را بررسی می‌کنیم.

کلیدواژه‌های فارسی مقاله	گروه موضعاً فشرده، توپولوژی موضعاً محدب، فضای لبگ وزندار، دوگان.

عنوان انگلیسی	A locally Convex Topology on the Beurling Algebras

چکیده انگلیسی مقاله	Introduction Let G be a locally compact group with a fixed left Haar measure λ and be a weight function on G; that is a Borel measurable function with for all . We denote by the set of all measurable functions such that ; the group algebra of G as defined in [2]. Then with the convolution product “” and the norm defined by is a Banach algebra known as Beurling algebra. We denote by n(G,) the topology generated by the norm . Also, let denote the space of all measurable functions 𝑓 with , the Lebesgue space as defined in [2]. Then with the product defined by , the norm defined by , and the complex conjugation as involution is a commutative algebra. Moreover, is the dual of . In fact, the mapping is an isometric isomorphism. We denote by the -subalgebra of consisting of all functions 𝘨 on G such that for each , there is a compact subset K of G for which . For a study of in the unweighted case see [3,6]. We introduce and study a locally convex topology on such that can be identified with the strong dual of . Our work generalizes some interesting results of [15] for group algebras to a more general setting of weighted group algebras. We also show that (,) could be a normable or bornological space only if G is compact. Finally, we prove that is complemented in if and only if G is compact. For some similar recent studies see [4,7,8,10,12-14]. One may be interested to see the work [9] for an application of these results. Main results* We denote by 𝒞 the set of increasing sequences of compact subsets of G and by ℛ the set of increasing sequences of real numbers in divergent to infinity. For any and , set and note that is a convex balanced absorbing set in the space . It is easy to see that the family 𝒰 of all sets is a base of neighbourhoods of zero for a locally convex topology on see for example [16]. We denote this topology by . Here we use some ideas from [15], where this topology has been introduced and studied for group algebras. Proposition 2.1 Let G be a locally compact group, and be a weight function on G. The norm topology n(G,) on coincides with the topology if and only if G is compact. Proposition 2.2 Let G be a locally compact group, and be a weight function on G. Then the dual of (,) endowed with the strong topology can be identified with endowed with -topology. Proposition 2.3 Let G be a locally compact group, and be a weight function on G. Then the following assertions are equivalent: a) (,) is barrelled. b) (,) is bornological. c) (,) is metrizable. d) G is compact. Proposition 2.4 Let G be a locally compact group, and be a weight function on G. Then is not complemented in ../files/site1/files/52/10.pdf

کلیدواژه‌های انگلیسی مقاله	Locally compact group, Locally convex topology, Weighted Lebesgue space, Dual.

نویسندگان مقاله	سعید مقصودی \| Saeid Maghsoudi University of Zanjan دانشگاه زنجان، گروه ریاضی

نشانی اینترنتی	http://mmr.khu.ac.ir/browse.php?a_code=A-10-80-1&slc_lang=fa&sid=1
فایل مقاله	فایلی برای مقاله ذخیره نشده است
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زبان مقاله منتشر شده	fa
موضوعات مقاله منتشر شده	جبر
نوع مقاله منتشر شده	مقاله مستقل

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