Identities in tensor products of Banach algebras
Identities in tensor products of Banach algebras
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Banach 代数张量积中的恒等式
DOI：
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发表时间：
1970
影响因子：
0.7
通讯作者：
R. J. Loy
中科院分区：
文献类型：
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作者：
R. J. Loy
设A1，A2是Banach代数，A1 <$A2是它们在复数域上的代数张量积.如果A1 <$A2上的代数范数是A1 <$A2，则A1 <$A2的<$A1 <$A2-完备化记为A1 <$A2。在本说明中，我们研究A1 α A2中恒等式和近似恒等式的存在性以及它们在A1和A2中的存在性。所得到的一些结果是已知的，但我们的证明方法似乎是新的，虽然它是相当初级的。
Let A1, A2 be Banach algebras, A1 ⊗ A2 their algebraic tensor product over the complex field. If ‖ · ‖α is an algebra norm on A1 ⊗ A2 we write A1 ⊗αA2 for the ‖ · ‖α-completion of A1 ⊗ A2. In this note we study the existence of identities and approximate identities in A1 ⊗αA2 versus their existence in A1 and A2. Some of the results obtained are already known, but our method of proof appears new, though it is quite elementary.