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We discuss renorming properties of the dual of a James tree space JT. Wepresent examples of weakly Lindelof determined JT such that JT* admits neitherstrictly convex nor Kadec renorming and of weakly compactly generated JT suchthat JT* does not admit Kadec renorming although it is strictly convexifiable.

Renormings of the dual of James tree spaces