2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59659Given an n-tuple {a_1, ..., a_n} of self-adjoint operators on an infinite dimensional Hilbert space H and a positive integer k, there exists a projection p of rank k such that, for each for j = 1, ..., n, pa_jp is a scalar multiple of p. Assuming that {a_1, ...,a_n, 1} is a linearly independent set in the Calkin algebra, then p can be chosen of infinite rank.12 pages, AMS TeXOperator Algebras47A13 (Primary), 15A99 (Secondary)text