This was described in 1956 by Horton and Whol in the paper Mass Communication and Para-social Interaction.

> One of the striking characteristics of the new mass media - radio, television, and the movies - is that they give the illusion of face-to-face relationship with the performer. [...] The most remote and illustrious men are met as if they were in the circle of one's peers; the same is true of a character in a story who comes to life in these media in an especially vivid and arresting way. We propose to call this seeming face-to-face relationship between spectator and performer a para-social relationship.

They even use your term 'persona' to refer to the individual behind the glass.

> But of particular interest is the creation by these media of a new type of performer: quizmasters, announcers, 'interviewers' in a new 'show-business' world - in brief, a special category of 'personalities' whose existence is a function of the media themselves. [...] Lacking an appropriate name for these performers, we shall call them personae.

http://visual-memory.co.uk/daniel/Documents/short/horton_and...