if 10 people own an item beshutfos, and the item is the type that does not get used up, e.g. a house, chair, table, land, etc. and one of the owners gives permission to use it, can the item be used by a non-owner, or do you need permission from all the owners?
and where is this halacha brought down?
It is not clear from your question what type of use the person wants to use. However as a general rule when someone has he permission of one of the owners, he is allowed to use it on a non permanent basis without asking permission from all the owners. This is because it is considered like the use of the owner in his property when his guest use it. This is especially true if it is a type of use that the other owners will not mind the other partner doing. However if it is a type of use or the circumstances are such that the other partners might mind, then you have to ask permission.
Pischei Choshen (Shutfus) 4-36 ftnt. 69.