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arXiv · 1608.00190

On the extendability of some classes of maps on Hilbert $C^*$-modules

Mohammad B. Asadi·Reza Behmani·Ali R. Medghalchi·Hamed Nikpey
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Abstract

In this paper, we show that every completely semi-$\phi$-map on a submodule of a Hilbert $C^*$-module has a completely semi-$\phi$-map extension on the whole of module. We also investigate the extendability of $\phi$-maps and provide examples of $\phi$-maps which has no $\phi$-map extension. Finally, we introduce a category of Hilbert $C^*$-module and determine injective objects in this category.

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Mohammad B. Asadi, Reza Behmani, Ali R. Medghalchi, Hamed Nikpey. 2016-07-31. On the extendability of some classes of maps on Hilbert $C^*$-modules. https://arxiv.org/abs/1608.00190

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