A short proof that B(L-1) is not amenable

Choi Yemon

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A short proof that B(L-1) is not amenable

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Non-amenability of B(E) has been surprisingly difficult to prove for the classical Banach spaces, but is now known for E = l(p) and E = L-p for all 1 <= p < infinity. However, the arguments are rather indirect: the proof for L-1 goes via non-amenability of l(infinity)(K(l(1))) and a transference principle developed by Daws and Runde (Studia Math., 2010). In this note, we provide a short proof that B(L-1) and some of its subalgebras are non-amenable, which completely bypasses all of this machinery. Our approach is based on classical properties of the ideal of representable operators on L-1, and shows that B(L-1) is not even approximately amenable.

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《Proceedings of the Royal Society of Edinburgh, Section A. Mathematics》 |2021年第6期|1758-1767|共10页
作者
Choi Yemon;
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作者单位

Univ Lancaster;

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原文格式 PDF
正文语种英语
中图分类数学;
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Amenable Banach algebras; Banach spaces; operator ideals; representable operators; GENERALIZED NOTIONS; BANACH-ALGEBRAS; NON-AMENABILITY; B(L(P));

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A short proof that B(L-1) is not amenable

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