Yusenko K. The structure theorems for *-algebras generated by the families of projections

The thesis is devoted to the subsequent development of the *-algebras connected with star-shaped graphs. Such algebras arise as the generalization of well-known H.Weyl's problem about the sum of two hermitian matrices. In work we investigate the case when the star-shaped graph is the extended Dynkin graph. For the case D_4 with tilde we got the full description of the parameters set for which the algebra has a *-representation. We also found the condition under which there exist one-to-one correspondence between irreducible representations and transitive systems of subspaces. For other extended Dynkin graphs we investigate the structure properties of the parameters set for which the corresponding algebras have *-representations. Given the condition under which such sets are infinite.