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Maghsoudi S. A locally Convex Topology on the Beurling Algebras. mmr 2019; 5 (2) :221-228

URL: http://mmr.khu.ac.ir/article-1-2556-en.html

URL: http://mmr.khu.ac.ir/article-1-2556-en.html

Let

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

. 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

We denote by

a) (,) is barrelled.

b) (,) is bornological.

c) (,) is metrizable.

d)

Type of Study: Original Manuscript |
Subject:
alg

Received: 2016/10/25 | Revised: 2019/12/16 | Accepted: 2018/06/27 | Published: 2019/11/18 | ePublished: 2019/11/18

Received: 2016/10/25 | Revised: 2019/12/16 | Accepted: 2018/06/27 | Published: 2019/11/18 | ePublished: 2019/11/18

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