The spectral decomposition property of the sum and product of two commuting operators (Q756682)

The sum and product of two commuting bounded spectral operators in a Hilbert space are spectral operators. This property generally does not extend to spectral operators in Banach spaces. In this paper, the authors indicate sufficient conditions for two commuting operators T and S to preserve the ``spectral decomposition property'' (SDP) under sum and product. One of the operators under consideration may be unbounded. Besides the SDP, the authors also investigate the behaviour of certain spectral-type analytic properties.