TY - JOUR
ID - 35964
TI - Some Properties of Continuous $K$-frames in Hilbert Spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Rahimlou, Gholamreza
AU - Ahmadi, Reza
AU - Jafarizadeh, Mohammad Ali
AU - Nami, Susan
AD - Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.
AD - Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
AD - Faculty of Physic, University of Tabriz,
Tabriz, Iran.
Y1 - 2019
PY - 2019
VL - 15
IS - 1
SP - 169
EP - 187
KW - $K$-frame
KW - c-frame
KW - c$K$-frame
KW - Local c$K$-atoms
DO - 10.22130/scma.2018.85866.432
N2 - The theory of continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory. The $K$-frames were introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of $K$-frames, there are many differences between $K$-frames and standard frames. $K$-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous $K$-frames or briefly c$K$-frames, namely some operators preserving and some identities for c$K$-frames. Also, the stability of these frames are discussed.
UR - https://scma.maragheh.ac.ir/article_35964.html
L1 - https://scma.maragheh.ac.ir/article_35964_7a67421bd91eead5fc7d70935aa2f7cb.pdf
ER -