Commuting n-tuples of closed operators which possess spectral capacity (Q1101662)

The paper studies the class of commuting n-tuples \(T=(T_ 1,T_ 2,...,T_ n)\) of closed operators and extends results due to J. Eschmeier and others for similar n-tuples of bounded operators. The notions of ``spectral decomposition property'' (SDP), ``spectral capacity'' (SC) and ``single valued extension property'' (SVEP) are defined and it is shown that the existence of SC implies the existence of SDP and hence SVEP. Also, if f is analytic in a neighbourhood of \(\sigma\) (T) and if T has SC then f has SC.