Spectral Synthesis of Jordan Operators

The purpose of this paper is to extend results of J. Wermer Ž1952, Proc. Amer. Math. Soc. 3, 270 277., L. Brown et al.Ž1960, Trans. Amer. Math. Soc. 96, 162 183., and D. SarasonŽ1972, J. Reine Agnew. Math. 252, 1 15; 1966, Pacific J. Math. 17, 511 517. on spectral subspaces of diagonalizable operators on separable complex Hilbert space to the class of so-called Jordan operators or infinite direct sums of Jordan cells.