(N,ε)-pseudospectra and condition (n,ε)-pseudospectra of an element pencil in a unital complex Banach algebra

As a continuation of the paper J. Math. Anal. Appl. 464(2018), 939-954. We will define and examine the $(n,\varepsilon)$-pseudospectra and condition $(n,\varepsilon)$-pseudospectra of an element pencil in a unital complex Banach algebra. We characterize the $(n,\varepsilon)$-pseudospectra of an element pencil in a unital complex Banach algebra. In particular, we demonstrate some properties of $(n,\varepsilon)$-pseudospectra and condition $(n,\varepsilon)$-pseudospectra of an element pencil in unital complex Banach algebras.