An Introduction to Neutrosophic Real Banach and Hillbert Spaces

Mehmet Celik , Necati Olgun

Department Of Mathematics, Gaziantep University, Gaziantep, Turkey

Emails: mathcelik@gmail.com;olgun@gantep.edu.tr  

Abstract

Banach and Hillbert spaces are the main important concepts in the study of classical functional analysis. This paper generalizes these two kinds of functional spaces into neutrosophic systems, where the concept of neutrosophic Banach space and neutrosophic Hillbert space will be defined and discussed for the first time over partial ordered neutrosophic spaces. Also, many related concepts such as neutrosophic Cauchy sequence, neutrosophic Bessel's inequality, and neutrosophic Parseval's identity will be established and proved.

Keywords: Neutrosophic Banach space; neutrosophic Hillbert space; neutrosophic inner product.