TY - JOUR ID - 251149 TI - On Some Properties of K-g-Riesz Bases in Hilbert Spaces JO - Wavelet and Linear Algebra JA - WALA LA - en SN - 2383-1936 AU - Shekari, Azam AU - Abdollahpour, Mohamad Reza AD - Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran AD - Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran. Y1 - 2022 PY - 2022 VL - 8 IS - 2 SP - 31 EP - 42 KW - K-Riesz basis KW - K-g-Riesz basis KW - g-orthonormal basis KW - right-invertible DO - 10.22072/wala.2021.535986.1341 N2 - In this paper, we study the K-Riesz bases and the K-g-Riesz bases in Hilbert spaces. We show that for $K \in B(\mathcal{H})$, a K-Riesz basis is precisely the image of an orthonormal basis under a bounded left-invertible operator such that the range of this operator includes the range of $K$. Also, we show that $\lbrace \Lambda_i \in B(\mathcal{H}, \mathcal{H}_i ) : \, i \in I \rbrace$ is a K-g-Riesz basis for $\mathcal{H}$ with respect to $\lbrace \mathcal{H}_i \rbrace_{i \in I}$if and only if there exists a g-orthonormal basis $\lbrace Q_i \rbrace_{i \in I}$for $\mathcal{H}$ and a bounded right-invertible operator $U $ on $\mathcal{H}$such that $\Lambda_i = Q_i U$ for all $i \in I$, and $R(K) \subset R(U^{*})$. UR - https://wala.vru.ac.ir/article_251149.html L1 - https://wala.vru.ac.ir/article_251149_92d637395b3105f77a85e0777f8443b4.pdf ER -