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• W1663412835 abstract "Let $mathcal H$ be a Hilbert space. Given a bounded positive definite operator $S$ on $mathcal H$, and a bounded sequence $mathbf{c} = {c_k }_{k in mathbb N}$ of nonnegative real numbers, the pair $(S, mathbf{c})$ is frame admissible, if there exists a frame ${ f_k }_{k in mathbb{N}} $ on $mathcal H$ with frame operator $S$, such that $|f_k |^2 = c_k$, $k in mathbb {N}$. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended version of Schur-Horn theorem, due to A. Neumann. We use this to get necessary conditions (and to generalize known sufficient conditions) for a pair $(S, mathbf{c})$ to be frame admissible." @default.
• W1663412835 created "2016-06-24" @default.
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• W1663412835 date "2007-04-01" @default.
• W1663412835 modified "2023-09-30" @default.
• W1663412835 title "The Schur-Horn theorem for operators and frames with prescribed norms and frame operator" @default.
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• W1663412835 doi "https://doi.org/10.1215/ijm/1258138428" @default.
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