Investigating Some Important Characteristics of Soft Hilbert Space

Abstract Main aim of this work is to discuss some important characteristics of soft Hilbert Space. In this present work we have analysed some important properties like orthogonality, orthonormality in soft Hilbert space. We discussed some examples of soft Hilbert space such as the soft space and some inequality results on this space have been given. Moreover, it has been demonstrated that each soft Hilbert space contains an orthonormal basis, which can be derived using the Gram–Schmidt orthogonalization procedure within a soft inner product space. AMS Classification: 03E72, 08A72