Amenability of Banach algebras of compact operators
Amenability of Banach algebras of compact operators
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紧算子的 Banach 代数的适用性
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
George A. Willis
中科院分区：
文献类型：
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作者：
Niels Gronbaek;Barry E. Johnson;George A. Willis
本文研究了紧算子的Banach algebraК(X)可服从的条件。我们给出了x的一个对称逼近性质，并证明了这个条件。这一性质被广泛的巴拿赫空间所满足，包括所有的经典空间。然后，我们研究了哪些由旧的Banach空间构造而成的新Banach空间保留了紧算子携带可调和代数的性质。粗略地说，对偶空间，前对偶空间和某些张量积继承了这个性质，而直接和没有。对于直接和，这个问题与线性算子的因式分解密切相关。在最后一节中，我们讨论了一些开放的问题，特别是关于适应性ofК(X)隐含了X的哪些性质的逆向问题。
In this paper we study conditions on a Banach spaceX that ensure that the Banach algebraК(X) of compact operators is amenable. We give a symmetrized approximation property ofX which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of new Banach spaces from old ones preserve the property of carrying amenable algebras of compact operators. Roughly speaking, dual spaces, predual spaces and certain tensor products do inherit this property and direct sums do not. For direct sums this question is closely related to factorization of linear operators. In the final section we discuss some open questions, in particular, the converse problem of what properties ofX are implied by the amenability ofК(X).