Just like a home, the only one who can make changes to a space is the owner (the person who claims the space). Not just whoever we say the owner is, no no no. The owner is an EVM-formatted address that is backed by a private key in any EIP-712 compatible wallet. Only actions signed by this private key can modify a space.
EIP-712 compliance in this case, however, does not mean that SpacesVM is an EVM or even an EVM derivative. SpacesVM is a new Avalanche-native VM written from scratch to optimize for storage-related operations.
Anyone can run their own SpacesVM instance to store spaces data and/or validate that any modifications that occur to spaces are only done by the owner.

