The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for -sums of finite-dimensional normed algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-5,
author = {P. Bharucha and R. J. Loy},
title = {Approximate and weak amenability of certain Banach algebras},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {195-204},
zbl = {1202.46053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-5}
}
P. Bharucha; R. J. Loy. Approximate and weak amenability of certain Banach algebras. Studia Mathematica, Tome 196 (2010) pp. 195-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-5/