TY - JOUR
ID - 47114
TI - $K$-orthonormal and $K$-Riesz Bases
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Ahmdi, Ahmad
AU - Rahimi, Asghar
AD - Department of Mathematics, Faculty of Science, University of Hormozgan, P.O.Box 7916193145, Bandar Abbas, Iran.
AD - Department of Mathematics, Faculty of Science, University of Maragheh, P.O.Box 55136-553, Maragheh, Iran.
Y1 - 2021
PY - 2021
VL - 18
IS - 1
SP - 59
EP - 72
KW - $K$-frame
KW - Riesz basis
KW - Orthonormal basis
KW - Atomic system
DO - 10.22130/scma.2020.130958.827
N2 - Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define theĀ $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.
UR - https://scma.maragheh.ac.ir/article_47114.html
L1 - https://scma.maragheh.ac.ir/article_47114_8902cf1717995f11537b68de849abfb0.pdf
ER -