Banach spaces lp(𝔹ℂ(N)) with the *-norm ∥.∥2,lp(𝔹ℂ(N)) and some properties

N. Sager, B. Sağir

In this work, we construct vector spaces lp(𝔹ℂ(N)) of absolutely p-summable *-bicomplex sequences with the *-norm ∥.∥2,lp(𝔹ℂ(N)) over the field ℂ(N). Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in 𝔹ℂ(N) with respect to ∥.∥2. 

Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 65-81