Isometries on conservative subalgebras of bounded sequences

Abstract

Using extreme point techniques, we show that if A A is a closed subalgebra of the bounded sequences which contain c c , then any linear isometry of A A onto itself is a permutation up to a modulus one multiplication. If the subalgebra A A is generated by an ideal, then a permutation P P maps A A onto itself if and only if P P maps μ \mu -null sets to μ \mu -null sets where μ \mu is a 0,1-valued finitely additive measure associated with the ideal. In particular, if T T is a nonnegative regular summability method, we characterize the isometries which map the bounded strongly T T -summable sequences onto themselves and give a concrete sufficient condition for a permutation to map the bounded strongly Cesaro summable sequences onto themselves.