بررسی فضاهای L_p(G) به‌عنوان گروه‌های برداری مشبکه توپولوژیکی

رنجبر, محمد علی; میرنوری, سید حسن

doi:10.22091/maa.2024.10266.1013

بررسی فضاهای L_p(G) به‌عنوان گروه‌های برداری مشبکه توپولوژیکی

نوع مقاله : مقاله پژوهشی

نویسندگان

¹ قم. آموزش‌وپرورش ناحیه چهارم

² گروه ریاضی، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

10.22091/maa.2024.10266.1013

چکیده

در این مقاله، فضاهای L_p(G) را با رابطۀ ترتیب نقطه‌ای به‌عنوان فضاهای ریس در نظر می‌گیریم و دسته‌ای از توپولوژی‌های گروهی (با عمل جمع) مشبکه‌ای را روی آن‌ها بررسی خواهیم کرد. این توپولوژی‌ها که توپولوژی‌های فیلتری مثبت و یا توپولوژی‌های زنجیره‌ای نام دارند، در بسیاری از مواقع توپولوژی برداری نیستند، بدین معنا که عمل ضرب اسکالر در آن‌ها پیوستۀ توأم نیست، ولی بسیاری از ویژگی‌های مورد انتظار را دارند.

کلیدواژه‌ها

موضوعات

آنالیز ریاضی و کاربردهای آن

عنوان مقاله [English]

On the L_p(G) spaces as topological lattice vector groups

نویسندگان [English]

Mohammad Ali Ranjbar ¹
Seyyed Hassan Myrnouri ²

¹ Teacher and free researcher

² Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

چکیده [English]

In this paper, we consider the L_p(G) spaces with pointwise ordering as Riesz spaces and investigate some lattice group topologies on them. In many cases, these topologies which are called link topologies or positive filter topologies are not vector topologies in the sense that the scalar multiplication is not continuous with respect to them, but they have many useful properties.

کلیدواژه‌ها [English]

ℓ-group. Unital ℓ-group
Order unit
Locally compact group
Haar measure
Riesz algebra
Topological lattice-ordered ring

مراجع

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