Non-closed sums of closed ideals in Banach algebras

by P.G.Dixon

1991 Mathematics Subject Classification: 46H10; 46J20, 46J15.


A major difficulty in Banach algebra theory is that sums of closed ideals need not be closed. We survey the known results and present examples showing that they are in most directions the best possible. We also give a new sufficient condition for closure in the uniform algebra setting.


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