Linear topological invariants of spaces of holomorphic functions in infinite dimension

It is shown that if $E$ is a Frechet space with the strong dual $E^*$ then $H_b(E^*)$, the space of holomorphic functions on $E^*$ which are bounded on every bounded set in $E^*$, has the property $(DN)$ when $E\in (DN)$ and that $H_b(E^*)\in(\Omega)$ when $E\in (\Omega)$ and either $E^*$ has an absolute basis or $E$ is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals $J(V)$ consisting of holomorphic functions on $E^*$ which are equal to $0$ on $V$ in $H(E^*)$ for every nuclear Frechet space $E$ with $E\in (DN)\cap (\Omega)$ is stablished when $J(V)$ is finitely generated by continuous polynomials on $E^*$

The linear invariants (dn ) and (Ω) for spaces of germs of holomorphic functions on compact subsets of Cn

For a compact subset K of Cn, we give necessary and sufficient conditions for [H(K)]0 to have the property (DN), and similarly for the property (Ω). We also show that H(D) is isomorphic to H(∆ n), where ∆n is the unit polydisc in Cn and D is any bounded Reinhardt domain in Cn. This last result requires a generalization of the classical Hartogs phenomenon

Repurposing existing medications for coronavirus disease 2019: protocol for a rapid and living systematic review

BACKGROUND Coronavirus disease 2019 (COVID-19) has no confirmed specific treatments. However, there might be in vitro and early clinical data as well as evidence from severe acute respiratory syndrome and Middle Eastern respiratory syndrome that could inform clinicians and researchers. This systematic review aims to create priorities for future research of drugs repurposed for COVID-19. METHODS This systematic review will include in vitro, animal, and clinical studies evaluating the efficacy of a list of 34 specific compounds and 4 groups of drugs identified in a previous scoping review. Studies will be identified both from traditional literature databases and pre-print servers. Outcomes assessed will include time to clinical improvement, time to viral clearance, mortality, length of hospital stay, and proportions transferred to the intensive care unit and intubated, respectively. We will use the GRADE methodology to assess the quality of the evidence. DISCUSSION The challenge posed by COVID-19 requires not just a rapid review of drugs that can be repurposed but also a sustained effort to integrate new evidence into a living systematic review. TRIAL REGISTRATION PROSPERO 2020 CRD42020175648

Some characterizations of the properties (DN) and (Ω~\tilde\Omega)

The aim of this paper is to show that 7816H_w(B,F) = H(B,F)7816 for every $\mathrm{LB}^\infty$-regular compact set $B$ in a Frechet space $E$ if and only if $F$ is a Frechet space having property (DN). At the same time, the equivalence between the existence of the $\mathrm{LB}^\infty$-regular compact set $B$ in a Schwartz-Frechet space $E$ with an absolute basis and the property $(\tilde\Omega)$ also established here