An orthogonality space is a set X together with symmetric and irreflexive binary relation ⊥, called the relation. A block partition of maximal mutually orthogonal elements X, decomposition collection subsets each which complement union others. (X,⊥) normal if any gives rise to unique space. The one-dimensional subspaces Hilbert equipped usual provides motivating example. Together maps that are,...

The purpose of this paper is to introduce and discuss the concept of orthogonality in the fuzzy metric spaces. At last we introduce and discuss the concept of orthogonality in the fuzzy normed spaces, and obtain some results on orthogonality in fuzzy normed spaces similar to orthogonality in normed spaces.

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given positive operator $A\in\B(\h)$, and number $\lambda\in [0,1]$, seminorm ${\|\cdot\|}_{(A,\lambda)}$ is defined set $\B_{A^{1/2}}(\h)$ in $\B(\h)$ having an $A^{1/2}$-adjoint. The combination sesquilinear form ${\langle \cdot, \...

Orthogonality or near-orthogonality is an important property in the design of experiments. Supersaturated designs are natural when we wish to investigate the main effects for a large number of factors but are restricted to a small number of runs. These supersaturated designs, by definition, cannot satisfy pairwise orthogonality of all the factor columns in the designmatrix. Hence, we need amean...