DANIEL SU ÁREZABSTRACT. Let A p be the Bergman space on the unit ball B n of C n for 1 < p < ∞, and T p be the corresponding Toeplitz algebra. We show that every S ∈ T p can be approximated by operators that are specially suited for the study of local behavior. This is used to obtain several estimates for the essential norm of S ∈ T p , an estimate for the essential spectral radius of S ∈ T 2 , and a localization result for its essential spectrum. Finally, we characterize compactness in terms of the Berezin transform for operators in T p .

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Hepatitis C virus (HCV) infection induces interferon (IFN)-stimulated genes (ISGs) and downstream innate immune responses. This study investigated whether baseline and on-treatment differences in these responses predict response versus virological breakthrough during therapy with direct-acting antivirals (DAAs). Thirteen HCV genotype 1b-infected patients who had previously failed a course of pegylated IFN/ribavirin were retreated with asunaprevir/daclatasvir for 24 weeks. After pretreatment biopsy, patients were randomized to undergo a second biopsy at week 2 or 4 on therapy. Microarray and NanoString analyses were performed on paired liver biopsies and analyzed using linear mixed models. As biomarkers for peripheral IFN responses, peripheral blood natural killer cells were assessed for phosphorylated signal transducer and activator of transcription 1 (pSTAT1) and tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) expression and degranulation. Nine of 13 (69%) patients achieved sustained virological response at 12 weeks off therapy (SVR12), and 4 experienced virological breakthroughs between weeks 4 and 12. Patients who achieved SVR12 displayed higher ISG expression levels in baseline liver biopsies and a higher frequency of pSTAT1 and TRAIL-expressing, degranulating natural killer cells in baseline blood samples than those who experienced virological breakthrough. Comparing gene expression levels from baseline and on-therapy biopsies, 408 genes (±1.2-fold, P < 0.01) were differentially expressed. Genes down-regulated on treatment were predominantly ISGs. Down-regulation of ISGs was rapid and correlated with HCV RNA suppression. Conclusion: An enhanced IFN signature is observed at baseline in liver and blood of patients who achieve SVR12 compared to those who experience a virological breakthrough; the findings suggest that innate immunity may contribute to clearance of HCV during DAA therapy by preventing the emergence of resistance-associated substitutions that lead to viral breakthrough during DAA therapy.

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