On Soft Dual Space of Soft Normed Spaces

TL;DR

This paper introduces the concept of soft dual spaces in soft normed spaces, exploring their properties and representation theorems, extending soft set theory into functional analysis.

Contribution

It defines soft dual spaces and operators, and proves a representation theorem for soft linear functionals in soft Hilbert spaces, advancing soft set theory applications.

Findings

Defined soft dual space and soft dual operator.

Proved representation theorem for soft linear functionals.

Extended soft set theory into soft Hilbert spaces.

Abstract

The concept of Soft set theory was introduced by Molodtsov in the study [8]. Soft real numbers and properties were introduced inthe study [6] and soft normed space was defined in [11]. In this study, firstly we obtain a soft normed space by defining a soft norm on (Real numbers) which is called soft normed real space. By using this normed space we define the soft linear functional and investigate some of its properties. Secondly, we introduce soft dual space and soft dual operator and investigate their properties. Finally, we state and prove the theorem about representation of soft linear functional by inner product in soft Hilbert spaces.