ANOTHER NOTE ON WEYLS THEOREM

''Weyl's theorem holds'' for an operator T on a Banach space X when th e complement in the spectrum of the ''Weyl spectrum'' coincides with t he isolated points of spectrum which are eigenvalues of finite multipl icity. This is close to, but not quite the same as; equality between t he Weyl spectrum and the ''Browder spectrum'', which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spe ctrum of polynomials in T. In this note we try to explore these distin ctions.