K’vod haRav, can one pick up a lost item to see if it has a siman (e.g. a name or phone number) without becoming responsible (shomer) for it? And if it has no siman, can one just leave it where it is, hoping that the owner will return for it? For example, a coat which has been left on a chair in shul for several weeks, in a large Jewish community. It is possible that the owner will remember and return to shul to get it. If I take it home and try to publicize the lost item, it is unlikely that the owner will find it, since there is no central place in the community to look for lost items. Thank you.
If one sees a lost item that seems to have a siman, he would be required to pick it up and attempt to return it to it’s rightful owner.
However, in a large community shul as you describe, you are not responsible to take it home and publicize it, as this will be no help in locating the owner. In addition, he may have left it it there with intent to keep it there. Perhaps putting up a sign on the shul bulletin board would help. If it has contact details, he should be notified.
In fact, an item such as this left for a long time in a public place, does not have to be returned at all according to the strict letter of the law, as we assume the owner already gave up hope of ever finding or retrieving it [see Y:D 262:5].