The ε-pseudospectra and the essential ε-pseudospectra of linear relations.

In the present paper, we introduce the new notions of the ε -pseudospectra and the essential ε -pseudospectra of linear relations and investigate their characterizations. Beside that, we establish the relationship between the pseudospectra (resp. essential ε -pseudospectra) of a sequence of closed linear relations and its limit in a Banach space. We finish by applying some obtained results of the essential ε -pseudospectra of transport equation. [ABSTRACT FROM AUTHOR]