A note on differences of composition operators acting on the Hardy space

When $\varphi$ and $\psi$ are holomorphic self-maps of the unit disk with bounded multiplicity, we give a compact characterization for the difference of composition operators $C_\varphi$ and $C_\psi$ acting on the Hardy space, which extends a recent result in the case of univalent maps by Choe et al

Differences of Weighted Composition Operators on

We study the boundedness and compactness of differences of weighted composition operators on weighted Banach spaces in the unit ball of CN

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Abstract We study the boundedness and compactness of differences of weighted composition operators on weighted Banach spaces in the unit ball of .</p

AAV-mediated lysophosphatidylcholine acyltransferase 1 (Lpcat1) gene replacement therapy rescues retinal degeneration in rd11

PURPOSE. The retinal degeneration 11 (rd11) mouse is a newly discovered, naturally occurring animal model with early photoreceptor dysfunction and rapid rod photoreceptor degeneration followed by cone degeneration. The rd11 mice carry a spontaneous mutation in the lysophosphatidylcholine acyltransferase 1 (Lpcat1) gene. Here, we evaluate whether gene replacement therapy using the fast-acting tyrosine-capsid mutant AAV8 (Y733F) can arrest retinal degeneration and restore retinal function in this model. METHODS. The AAV8 (Y733F)-smCBA-Lpcat1 was delivered subretinally to postnatal day 14 (P14) rd11 mice in one eye only. At 10 weeks after injection, treated rd11 mice were examined by visually-guided behavior, electroretinography (ERG) and spectral domain optical coherence tomography (SD-OCT), and then killed for morphologic and biochemical examination. RESULTS. Substantial scotopic and photopic ERG signals were maintained in treated rd11 eyes, whereas untreated eyes in the same animals showed extinguished signals. The SD-OCT (in vivo) and light microscopy (in vitro) showed a substantial preservation of the outer nuclear layer in most parts of the treated retina only. Almost wild-type LPCAT1 expression in photoreceptors with strong rod rhodopsin and M/S cone opsin staining, and normal visuallyguided water maze behavioral performances were observed in treated rd11 mice. CONCLUSIONS. The results demonstrate that the tyrosine-capsid mutant AAV8 (Y733F) vector is effective for treating rapidly degenerating models of retinal degeneration and, moreover, is more therapeutically effective than AAV2 (Y444, 500, 730F) vector with the same promotercDNA payload. To our knowledge, this is the first demonstration of phenotypic rescue by gene therapy in an animal model of retinal degeneration caused by Lpcat1 mutation