Suppose In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark) if there is a closed bijective linear map between dense subspaces preserving the group action.
Can we infer that "An open bijective linear map will satisfy the requirements of Naimark equivalence in no circumstances"? Yes, no, or maybe?
Suppose In mathematical representation theory, two representations of a group on topological vector spaces are called Naimark equivalent (named after Mark Naimark) if there is a closed bijective linear map between dense subspaces preserving the group action. Can we infer that "An open bijective linear map will satisfy the requirements of Naimark equivalence in no circumstances"? Yes, no, or maybe?