When do all bounded linear operators attain their norm?
Mingu Jung (Pohang University of Science and Technology, Republic of Korea)
In this talk, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in L(E,F). By using a theorem due to Pfitzner on James boundaries, we show that if there exists a relatively compact set K of L(E,F) (in the weak operator topology) such that 0 is an element of its closure (in the weak operator topology) but it is not in its norm closed convex hull, then we can guarantee the existence of an operator which does not attain its norm. This allows us to provide the following generalization of results due to Holub and Mujica. We also present a characterization of the Schur property in terms of norm-attaining operators.
6. mail kell 10.00. Liitu Zoomis.
ID: 952 2966 4082
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