Shifts on products of banach spaces

Abstract

It is well-known in the literature that the product of two Banach spaces does not necessarily admit a shift even with the case where each factor has a shift. The purpose of this paper is to explicitly construct a complex shift on the product of Banach spaces, c and c ₀. Furthermore, we show that the product spaces c × ℓ ^p and c ₀ × ℓ ^p , 0 ≤ p ≤ ∞ admit a complex shift.