LINEAR FUCTIONALS ON $O_n$ ASSOCIATED TO UNIT VECTORS

LINEAR FUCTIONALS ON $O_n$ ASSOCIATED TO UNIT VECTORS

We study the vectors related tro states on the Cuntz algebra Ο(sub)n and prove hat, for tow states $\omega$ and $\rho$ on Ο(sub)n with $\omega$│UHF(sub)n = $\rho$│UHF(sub)n, if ($\omega$(s$_1$), …, $\omega$(s(sub)n)) and ($\rho$(s$_1$),…, $\rho$(s(sub)n)) are unit vectors, then they and linearly dependent. We also study the linear functional on Ο(sub)n associated to a sequence of unit vectors in C(sup)n which is the generalization of the Cuntz state. We show that if the linear functional associated to a sequence of unit vectors with a certain condition is a state, then it is just the Cuntz state.