# Riesz bases from orthonormal bases by replacement

29 Apr 2018 De Carli Laura Edward Julian

Given an orthonormal basis ${\mathcal V}= \{v_j\} _{j\in N}$ in a separable Hilbert space $H$ and a set of unit vectors ${\mathcal B}=\{w_j\}_{j\in N}$, we consider the sets ${\mathcal B}_N$ obtained by replacing the vectors $v_1, ...,\, v_N$ with vectors $w_1,\, ...,\, w_N$. We show necessary and sufficient conditions that ensure that the sets ${\mathcal B}_N$ are Riesz bases of $H$ and we estimate the frame constants of the ${\mathcal B}_N$... (read more)

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