We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give an example (due to J. F. Feinstein) of a non-compact, bounded derivation from a uniform algebra A into a symmetric A-bimodule.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-11,
author = {Matthew J. Heath},
title = {Compactness of derivations from commutative Banach algebras},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {191-198},
zbl = {1216.46044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-11}
}
Matthew J. Heath. Compactness of derivations from commutative Banach algebras. Banach Center Publications, Tome 89 (2010) pp. 191-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-11/