C*-algebras generated by orthogonal projections and their applications

We study the following problem: Given a Hilbert spaceH and a set of orthogonal projectionsP, Q1, ..., Qn on it, with the conditionsQj·Qk=δj,kQk,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$j,k = \overline {1,n,} \sum\nolimits_{k = 1}^n Q _k = I$$ \end{document}, describe theC*-algebraC*(P, Q1, ..., Qn) generated by these projections.