The orthogonality in 2-Hilbert Spaces

In this paper, first, we introduce the new concept of (complex) 2-Hilbert spaces, that is, we define the concept of 2-inner product spaces with a complex valued 2-inner product by using the 2-norm. Next, we prove some theorems on orthogonality and related important properties. Finally, we give some open problems related to 2- Hilbert spaces.