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Paper IPM / M / 15578  


Abstract:  
We study the BishopPhelpsBollobÃ¡s property for operators from ï¿½??4ï¿½?? to a Banach space. For this reason we introduce an appropiate geometric property, namely the AHSpï¿½??4ï¿½??. We prove that spaces Ysatisfying AHSpï¿½??4ï¿½?? are precisely those spaces Y such that (ï¿½??4ï¿½??,Y) has the BishopPhelpsBollobÃ¡s property. We also provide classes of Banach spaces satisfying this condition. For instance, finitedimensional spaces, uniformly convex spaces, C0(L) and L1(Î¼) satisfy AHSpï¿½??4ï¿½??.
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