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 Hom∗A(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.
AMS Subject Classification: Primary 42C15; 46L05
In this paper, we present some properties of K-operator Frame in Hilbert $C^{\ast}$-modules.Topics that will be discussed include: K-operator Frame and Dual K-operator frame in Hilbert $C^{\ast}$-modules.We will also study K-operator Frame in two Hilbert $C^{\ast}$-modules with different $C^{\ast}$-algebras.
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