Nonexistence of category-(c) normalizable frames

Let $H$ be a Hilbert space, and let category (c) be the class of frames described in Theorem of the source. A frame is normalizable when normalizing each nonzero vector produces a frame, namely when $(x_n/\|x_n\|)$ is a frame. Nonexistence conjecture. There does not exist a normalizable frame belonging to category (c) in Theorem. The conjecture concerns the remaining case in the paper's classification of normalizable frames; no resolution is supplied in the given text.