A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras.
Sia un compatto, una funzione analitica all'intorno di , ed la massima molteplicità in degli zeri di ; si prova che la potenza (, ) è integrabile in . L'estensione meromorfa dell'applicazione da a tutto (con valori in anziché in ) era già stata provata in [1] e [2].
For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator , 0 < s < 2, to be the linear extension of the map , where denotes the -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that is bounded on , then for all 0 < s < 2 the operator is bounded on .
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.