Geodesic
Approximate Identities in Banach Algebras of Compact Operators
Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 45-53

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a Banach space and let A be a uniformly closed algebra of compact operators on X, containing the finite rank operators. We set up a general framework to discuss the equivalence between Banach space approximation properties and the existence of right approximate identities in A. The appropriate properties require approximation in the dual X* by operators which are adjoints of operators on X. We show that the existence of a bounded right approximate identity implies that of a bounded left approximate identity. We give examples to show that these properties are not equivalent, however. Finally, we discuss the well known result that, if X* has a basis, then X has a shrinking basis. We make some attempts to generalize this to various bounded approximation properties.
DOI : 10.4153/CMB-1993-008-8
Mots-clés : 46B28, 46H20, 47D30, 47D50 
Grønbæk, Niels; Willis, George A. Approximate Identities in Banach Algebras of Compact Operators. Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 45-53. doi: 10.4153/CMB-1993-008-8
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