Approximation of p-summing operators by adjoints

Reinov, Oleg I.
May 2012
AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p32
Academic Journal
We consider the following question for the ideals Πp of absolutely p-summing operators: Is it true that, for given Banach spaces X and Y, the unit ball of the space Πp(X,Y) is dense, for some natural topology, in the unit ball of the space Πp(X,Y**) or in the unit ball of the corresponding space Πpdual(Y*,X*): = {U:Y*→X*|U*|XƸΠp(X,Y**)}? As 'natural topologies', we consider strong and weak operator topologies, compact-open topology, topology of X × Y*-convergence etc.


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