# Compactness of derivations from commutative Banach algebras

Banach Center Publications (2010)

- Volume: 91, Issue: 1, page 191-198
- ISSN: 0137-6934

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topMatthew 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 -

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