@article {
author = {Naroei Irani, Mona and Nazari, Akbar},
title = {Some Properties of $ \ast $-frames in Hilbert Modules Over Pro-C*-algebras},
journal = {Sahand Communications in Mathematical Analysis},
volume = {16},
number = {1},
pages = {105-117},
year = {2019},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.75253.328},
abstract = {In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ \mathcal{A} $ into a Hilbert $ \mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ \mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ \ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ \ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ \{ {h_i} \}_{i \in I} }$ is a standard $ \ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ \ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ \ast $-frames in Hilbert modules over pro-C*-algebras are studied.},
keywords = {Hilbert modules over pro-C*-algebras,Standard $ ast $-frame of multipliers,$ ast $-frame operator,Pre-$ ast $-frame},
url = {https://scma.maragheh.ac.ir/article_36278.html},
eprint = {https://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf}
}