We report a deep search for redshifted HI 21 cm emission from three damped and sub-damped Lyman-$alpha$ absorbers (DLAs) at $z approx 0.1$ with the Green Bank Telescope (GBT). No evidence for a redshifted HI 21 cm emission signal was obtained in the GBT spectra of two absorbers, with the data on the third rendered unusable by terrestrial interference. The non-detections of HI 21 cm emission yield strong constraints on the HI masses of the associated galaxies, M$_{rm HI} < 2.3 times 10^9 times (Delta V/100)^{1/2}$ M$_odot$ for the sub-DLA at $z = 0.0830$ towards J1553+3548, and M$_{rm HI} < 2.7 times 10^9 times (Delta V/100)^{1/2}$ M$_odot$ for the DLA at $z = 0.0963$ towards J1619+3342, where $Delta V$ is the HI 21 cm line width, in km s$^{-1}$. This continues the trend of low HI masses found in all low-$z$ DLAs and sub-DLAs that have been searched for redshifted HI 21 cm emission. Low-redshift absorbers with relatively low HI column densities, $lesssim few times 10^{20}$ cm$^{-2}$, thus do not typically arise in massive gas-rich galaxies.
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