$\ast$-Operator frame for $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$

TL;DR

This paper introduces the concept of $ ext{ extasterisk}$-operator frames in Hilbert pro-$C^{ ext{ extasterisk}}$-modules, generalizing $ ext{ extasterisk}$-frames, and explores their properties and tensor products.

Contribution

It presents the new concept of $ ext{ extasterisk}$-operator frames and studies their properties and tensor products in the context of Hilbert pro-$C^{ ext{ extasterisk}}$-modules.

Findings

Defined $ ext{ extasterisk}$-operator frames in Hilbert pro-$C^{ ext{ extasterisk}}$-modules.

Established key properties of $ ext{ extasterisk}$-operator frames.

Analyzed tensor products of $ ext{ extasterisk}$-operator frames.

Abstract

In this Work, We introduce the concept of $\ast$-operator frame, which is a generalization of $\ast$-frames in Hilbert pro-$C^{\ast}$-modules, and we establish some results, we also study the tensor product of $\ast$-operator frame for Hilbert pro-$C^{\ast}$-modules.