A person may wear a tallis gadol or katon in a reshus harabim on Shabbos. Since the tzitzis strings are a necessary component of the garment, they are considered part of the garment and one is not carrying by wearing it. Even if the garment is only required to have tzitzis mid’rabonon, a person can still wear it in the reshus harabim. Although there is no obligation to wear tzitzis at night, they can be worn outside on Friday nights. When a tallis is worn outside, care must be taken to wear it properly. Otherwise, the garment is viewed as being carried and not worn.
[שו"ע יג, ב, ומשנ"ב ד ו־ו; ביאורים ומוספים דרשו, 6 ,7 ו־9 ;וראה שו"ע ט, א]