Compactness of derivations from commutative Banach algebras

Matthew J. Heath

Banach Center Publications (2010)

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

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.