某些Banach代数上的诱导拓扑

Pub Date : 2023-01-01 DOI:10.2298/fil2304311e

M. Eshaghi, A. Ghaffari, M. Sahabi

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引用次数: 0

摘要

设A是一个有界近似恒等式以1为界的巴拿赫代数。在a上引入了两种新的拓扑——so和wo。我们研究了这两种拓扑，并将它们相互比较，并与范数拓扑进行了比较。然后进一步研究了?so和?wo的性质，并注意了局部紧群G的群代数L1(G)，得到了局部紧群G是有限的各种充要条件。

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Induced topologies on certain Banach algebras

Let A be a Banach algebra with a bounded approximate identity bounded by 1. Two new topologies ?so and ?wo are introduced on A. We study these topologies and compare them with each other and with the norm topology. The properties of ?so and ?wo are then studied further and we pay attention to the group algebra L1(G) of a locally compact group G. Various necessary and sufficient conditions are found for a locally compact group G to be finite.

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