Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, P. O. Box 98135-674, Zahedan, Iran
10.22034/kjm.2022.355505.2629
Abstract
We study those Bessel sequences $\{f_k\}_{k=1}^{\infty}$ in an infinite-dimensional, separable Hilbert space $H$ for which the operator $S$ defined by $Sf:=\sum_{k=1}^{\infty} \langle f,f_k\rangle f_k$ is of the form $cI+T$, for some real number $c$ and a bounded linear operator $T$, where $I$ denotes the identity operator. We use a reverse Schwarz inequality to provide conditions on $T$ and $c$ that allow $\{f_k\}_{k=1}^{\infty}$ to be a frame. Moreover, we introduce and study frames whose frame operators are compact (respectively, finite-rank) perturbations of constant multiples of the identity, frames to which we refer as compact-tight (respectively, finite-rank-tight) frames. As our final result, we prove a theorem on the weaving of certain compact-tight frames.
Movahed, S., Hosseini Giv, H., & Ahmadi Ledari, A. (2023). A study of Bessel sequences and frames via perturbations of constant multiples of the identity. Khayyam Journal of Mathematics, 9(1), 102-115. doi: 10.22034/kjm.2022.355505.2629
MLA
Sima Movahed; Hossein Hosseini Giv; Alireza Ahmadi Ledari. "A study of Bessel sequences and frames via perturbations of constant multiples of the identity". Khayyam Journal of Mathematics, 9, 1, 2023, 102-115. doi: 10.22034/kjm.2022.355505.2629
HARVARD
Movahed, S., Hosseini Giv, H., Ahmadi Ledari, A. (2023). 'A study of Bessel sequences and frames via perturbations of constant multiples of the identity', Khayyam Journal of Mathematics, 9(1), pp. 102-115. doi: 10.22034/kjm.2022.355505.2629
VANCOUVER
Movahed, S., Hosseini Giv, H., Ahmadi Ledari, A. A study of Bessel sequences and frames via perturbations of constant multiples of the identity. Khayyam Journal of Mathematics, 2023; 9(1): 102-115. doi: 10.22034/kjm.2022.355505.2629