s Saboori - Payame Noor University
f Ershad. - Payame Noor University

Let AandBbe two complex unital Banach algebras and BAT→: be a bounded linear map. For ∈n , define ()()()()()(),......,...,,,212121nnnaTaTaTaaaTaaanT−=∨ For all Aaaan∈,...,,21. If ()naanT...,1δ≤∨ for some 0> δ, then T is called an approximately n-multiplicative linear map. It is of interest whether or not this implies thatT is near to an n-multiplicative linear map. The pair ()BA, is called an AMNMn− pair, if approximately n-multiplicative linear maps are near to n- multiplicative linear maps. In this note we discuss this definition and show that, for some Banach algebras A and B, ()BA, is an AMNMn− pair. Also we consider that Abe the product of Banach algebras and =B.

Banach algebras, Approximately n-multiplicative maps, AMNMn− pair