A triangle inequality in Hilbert modules over matrix algebras

Abstract

The matrix-valued triangle inequalities of R.C. Thompson [Pacific J. Math. 66 (1976) 285–290] are extended to sequences of matrices with real, complex, or quaternion entries. These new matrix inequalities, in turn, imply a natural formulation of the triangle inequality which is valid in certain Hilbert modules over real or complex semisimple matrix algebras.