This book provides the foundations for a rigorous theory of functional analysis with
bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and …

With the goal of providing the foundations for a rigorous study of modules of bicomplex
holomorphic functions, we develop a general theory of functional analysis with bicomplex …

Any bounded linear operator between real (quasi-) Banach spaces T: X→ Y has a natural
bounded complex linear extension TC: XC→ YC defined by the formula TC (x+ iy)= Tx+ iT y …

In this work we discuss quaternionic inner product spaces. In particular we consider the
quaternionic extensions of real inner product spaces and we give a characterization of the …

Résumé Nous considérons des opérateurs linéaires bornés définis sur des espaces normés
réels, et dont les images sont dans des espaces quaternioniques. Nous étudions les normes …

On various occasions, when working with quaternionic linear spaces, there is a need to
restrict them to their complex linear structure, then it becomes essential to understand …

Continuing our previous research we consider here the internal quaternionization of real
and complex linear spaces; categories of quaternionic linear spaces, and decompositions of …

We study the connections between the norms of bounded operators on real and complex
normed spaces, and with range in quaternionic spaces, and of their quaternionic extensions …

This work is a continuation of our work [14] where we considered linear spaces in the
following two situations: a real space admits a multiplication by complex scalars without …

This work is a continuation of our work [12] where we considered linear spaces in the
following two situations: a real space admits a multiplication by complex scalars without …