ESTIMATION OF A PARTIAL INVOLUTION IN A BANACH ALGEBRA

Let A be a complex Banach algebra with identity element 1, let paralle l to 1 parallel to = 1, and let parallel to xy parallel to less than o r equal to parallel to x parallel to.parallel to y parallel to for any x, y is an element of A. If a, b is an element of A are Hermitian (i. e., parallel to exp ita parallel to = parallel to exp ita parallel to = 1 for any real t), then parallel to a -ib parallel to less than or e qual to gamma parallel to a + ib parallel to, where gamma = 1.92 +/- 0 .04. Clarifications are given.