Vyacheslav RABANOVYCH
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.