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arXiv · 2212.01177

Douglas' factorization theorem and atomic system in Hilbert pro$-C^{\ast}-$module

Mohamed Rossafi·Roumaissae Eljazzar·Ram Mohapatra
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Abstract

In the present paper we introduce the generalized inverse operators which have an interesting role in operator theory. We establish Douglas' factorization theorem type for Hilbert pro-$C^{\ast}$-module. We introduce the notion of atomic system and of $K$-frame in Hilbert pro-$C^{\ast}$-module and we study the relationship between them. We also demonstrat some properties of $K$-frame by using Douglas' factorization theorem.Finally we demonstrate that the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain conditions is once again a $K$-frame.

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Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra. 2022-09-18. Douglas' factorization theorem and atomic system in Hilbert pro$-C^{\ast}-$module. https://arxiv.org/abs/2212.01177

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