# PSEUDO n-JORDAN HOMOMORPHISMS AND PSEUDO n-HOMOMORPHISMS ON BANACH ALGEBRAS

• Accepted : 2020.04.02
• Published : 2020.06.25

#### Abstract

In this paper, we correct some errors and typos of [2] and introduce a new concept related to pseudo n-Jordan homomorphisms, that we call it pseudo n-homomorphism. We investigate automatic continuity and positivity of pseudo n-homomorphisms and pseudo n-Jordan homomorphisms on Banach algebras and C*-algebras. Moreover, we show that the sum of two pseudo n-Jordan homomorphisms is not a pseudo n-Jordan homomorphism and we show that under some conditions the sum of two pseudo n-Jordan homomorphisms is a pseudo n-Jordan homomorphism.

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