On the Inner-Product Spaces of Complex Interval Sequences

Abstract

In recent years, there has been increasing interest in interval analysis. Thanks to interval numbers, many real world problems have been modeled and analyzed. Especially, complex intervals have an important place for interval-valued data and interval-based signal processing. In this paper, firstly we introduce the notion of a complex interval sequence and we present the complex interval sequence spaces $\mathbb{I}(w)$ and $\mathbb{I}(l_{p})$, $1\leq p<\infty$. Secondly, we show that these sequence spaces have an algebraic structure called quasilinear space. Further, we construct an inner-product on $\mathbb{I}(l_{2})$ and we show that $\mathbb{I}(l_{2})$ is an inner-product quasilinear space.