A note on Markuševič bases in weakly compactly generated Banach spaces
In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
2000 Mathematics Subject Classification: 44A40, 42A38, 46F05The product of an entire function satisfying a growth condition at infinity and an integrable Boehmian is defined. Properties of this product are investigated.
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...
In this note we study sets of normal generators of finitely presented residually -finite groups. We show that if an infinite, finitely presented, residually -finite group is normally generated by with order , then where denotes the first -Betti number of . We also show that any -generated group with must have girth greater than or equal .