A remark on averaging operators on homogeneous spaces

To any sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ g_1,..., g_d, g{-1 \atop 1},..., g{-1 \atop d} $\end{document} in a group G one can associate an averaging operator acting on functions on a homogeneous space of G. For a connected compact Lie group G we obtain a lower bound for the L2-norm of this operator in the orthocomplement to the constants.