STABILITY OF RIESZ BASES

The Kato Theorem on similarity for sequences of projections in a Hilbert space is extended to the case when both sequences consist of non-selfadjoint projections. Passing to subspaces, this leads to stability theorems for Riesz bases of subspaces, at least one of which is finite dimensional, and for arbitrary vector Riesz bases. The following is proved as an application. If{phi(n)}(n-1)(infinity) is a Riesz basis and vertical bar theta(n)vertical bar <= C for large n, where the constant C depends only on {phi(n)}(n-1)(infinity), then {phi(n)+theta(n)phi(n)+1}(n-1)(infinity) also forms a Riesz basis.