On a paper by Khmyleva and Bukhtina

It is well know that every separable Hilbert space possesses an orthonormal Schauder bases, i.e. a Schauder bases $\{x_n\}_{n=1}^\infty$, for which $||x||=1$ and $(x_n,x_m)=0$ for any $n, m\in N$, $n\ne m$. In this note, we consider a sequence of elements in a Hilbert space for which angles between any two terms are equal and different from zero. Basicity and some other properties of such systems are investigated. In particular, a short proof of a result by Khmyleva and Bukhtina is provided and a more general form of this result is stated.