2022/12/14 by Roumaissae Eljazzar, Eljazzar, Roumaissae, Mohamed Rossafi +3
Mathematics · #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2212.07004
The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators HomA∗(X) on a Hilbert pro-C∗-module X. The analysis operator, the synthesis operator and the frame operator are presented. Secondly, we study the stability of operator frame under small perturbations. We also study the tensor product of operator frame for Hilbert pro-C∗-modules. Finally, we establish its dual and some properties.