Maps preserving the pseudo spectrum of generalized product of operators

Let be the algebra of all bounded linear operators acting on a complex Hilbert space with dim . For an integer k ≥ 2, let (i1 , … , im) be a finite sequence such that {i1 , … , im} = {1, … , k} and at least one of the terms in (i1 , … , im) appears exactly once. A generalized product of operators A1, … , Ak ∈ is defined byFix ϵ > 0, and let σϵ (A) denote the ϵ-pseudo spectrum of an operator . In this paper, we characterize the form of all surjective maps that satisfy