Abstract: Orthogonal decomposition theorem plays an important role in linear functional analysis. In the present paper, we give partial orthogonal decomposition theorem which is the quasilinear counterpart of the orthogonal decomposition theorem given in linear inner product spaces. Also, we prove some new theorems on inner product quasilinear spaces. Further, we provide examples to illustrate our results. Our results generalize some well-known results in linear functional analysis.
Keywords: Quasilinear space, Normed quasilinear spaces, Inner product quasilinear space, Hilbert quasilinear space, orthogonality, orthonormality.
How to cite this article:
Hacer Bozkurt and Yilmaz Yilmaz, Further Results on Inner Product Quasilinear Spaces, International Journal of Advances in Mathematics, Volume 2019, Number 3, Pages 34-44, 2019.