A note on comprehensive backward biorthogonalization.
If is a finite measure space and a Banach space, in this note we show that , the Banach space of all classes of weak* equivalent -valued weak* measurable functions defined on such that a.e. for some equipped with its usual norm, contains a copy of if and only if contains a copy of .
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson’s property (), Talponen’s countable separation property, or being a Gâteaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, the question whether the duals of nonseparable Lipschitz-free spaces have a weak sequentially compact ball is undecidable in ZFC. Finally, we provide an...
The - regularity of the gradient of weak solutions to nonlinear elliptic systems is proved.