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We give an example of a locally A-convex algebra which is neither m-convex nor uniformly ^-convex. This example is used to answer some questions on ^-convex algebras (see symbol 4). We especially show that Michael's problem (in m-convex algebras) is equivalent to the same problem in A-convex algebras. Finally some questions on bounded sets in A-convex algebras are studied.doi:10.1090/s0002-9939-1990-1014641-8 fatcat:sp6ysjonwjh5za5qlamfcupavu