A Systematic Study of Frame Sequence Operators and their Pseudoinverses - Mathematics > Functional Analysis

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Abstract: In this note we investigate the operators associated with frame sequences ina Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}\mathbb{N} \toH$, the analysis operator $T^{\ast}:H\to$ $% \ell ^{2}\mathbb{N}$ and theassociated frame operator $S=TT^{\ast}$ as operators defined on or to thewhole space rather than on subspaces. Furthermore, the projection $P$ onto therange of $T$, the projection $Q$ onto the range of $T^{\ast}$ and the Grammatrix $G=T^{\ast}T$ are investigated. For all these operators, we investigatetheir pseudoinverses, how they interact with each other, as well as possibleclassification of frame sequences with them. For a tight frame sequence, weshow that some of these operators are connected in a simple way.

Autor: P. Balazs, M. A. El-Gebeily

Fuente: https://arxiv.org/