Differential geometry of systems of projections in Banach algebras

Gustavo Corach, Horacio Porta and Lázaro Recht

Vol. 143 (1990), No. 2, 209–228

DOI: 10.2140/pjm.1990.143.209

Abstract

Let A be a Banach algebra, n a positive integer and Q_n = {(q₁,…,q_n) ∈ Aⁿ : q_iq_k = δ_ikq_i, q₁ + ⋯ + q_n = 1}. The differential geometry of Q_n, as a discrete union of homogeneous spaces of the group G of units of A is studied, a connection on the principal bundle G → Q_n is defined and invariants of the associated connection on the tangent bundle TQ_n are determined.

Mathematical Subject Classification 2000

Primary: 46H99

Secondary: 46M20, 58B25

Milestones

Received: 26 May 1987

Revised: 15 April 1989

Published: 1 June 1990