Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

Ukraine

E-mail: slavik@imath.kiev.ua

**On infinite dimensional representations of *-algebras
generated by five orthoprojections with a linear relation and an orthogonality
relation**

**Abstract:**

We investigate *-algebras generated by five orthoprojections $p_1,\ldots,p_5$
which satisfy a linear relation $p_1+p_2+p_3+p_4+ap_5=be$ for some
real numbers a and b, e is the identity element and an orthogonality relation
$p_4p_5=0$. We find infinite dimensional irreducible representations of
such algebras for special cases.