Exploring Non-Newtonian Hilbert Spaces

Abstract

Non-Newtonian Hilbert spaces offer a novel framework for exploring mathematical structures beyond classical Newtonian paradigms. This paper delves into the rich landscape of operators within such spaces, investigating their fundamental properties, behavior, and implications. By extending the traditional concepts of operators from standard Hilbert spaces to the non-Newtonian realm, we uncover unique characteristics that redefine the dynamics of linear transformations. Through a comprehensive analysis, we elucidate the distinct features of operators operating on non-Newtonian Hilbert spaces, shedding light on their applications across diverse fields, including quantum mechanics, functional analysis, and signal processing. This exploration not only broadens the theoretical foundations but also opens avenues for innovative applications in various scientific domains. In this paper we remind vector spaces over real and complex non-Newtonian field with respect to the − calculus, the definitions of real and complex inner product spaces and Hilbert spaces which are special type of normed space and complete inner product spaces in the sense of − calculus. Finally, by using the − norm properties of complex structures, we examine the bounded linear operators on non-Newtonian Hilbert spaces.