Compactness of derivations from commutative Banach algebras

Matthew J. Heath. "Compactness of derivations from commutative Banach algebras." Banach Center Publications 91.1 (2010): 191-198. <http://eudml.org/doc/282286>.

@article{MatthewJ2010,
abstract = {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.},
author = {Matthew J. Heath},
journal = {Banach Center Publications},
keywords = {compact derivations; weakly compact derivations; symmetric -bimodule},
language = {eng},
number = {1},
pages = {191-198},
title = {Compactness of derivations from commutative Banach algebras},
url = {http://eudml.org/doc/282286},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Matthew J. Heath
TI - Compactness of derivations from commutative Banach algebras
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 191
EP - 198
AB - 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.
LA - eng
KW - compact derivations; weakly compact derivations; symmetric -bimodule
UR - http://eudml.org/doc/282286
ER -