TY - JOUR
ID - 36278
TI - Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Naroei Irani, Mona
AU - Nazari, Akbar
AD - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
AD - Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Y1 - 2019
PY - 2019
VL - 16
IS - 1
SP - 105
EP - 117
KW - Hilbert modules over pro-C*-algebras
KW - Standard $ ast $-frame of multipliers
KW - $ ast $-frame operator
KW - Pre-$ ast $-frame
DO - 10.22130/scma.2018.75253.328
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_36278.html
L1 - https://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf
ER -