—。
Restricted Area — Entry Without Permission Forbidden.
Literal
Controlled area — permission without-[classical negative-なくして] entry [object-を] forbid-[classical-ず].
Classical/administrative sign register. 許可なくして uses the classical negative form なくして ('without having'), a set literary alternative to 許可なしで. 禁ず is the classical/literary ending of 禁じる 'to forbid' — both the なくして negation and the terminal ~ず are 文語 (bungo, classical written language) remnants preserved in formal signage and legal notices precisely because of their terseness and authority. 立ち入り 'entry' is a verbal noun from the compound verb 立ち入る 'to enter, intrude.'