Geodesic
The spectrum of orthogonal sums of subnormal pairs
Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 11-15

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This note provides yet another example of the difficulties that arise when one wants to extend the spectral theory of subnormal operators to subnormal tuples. Several basic properties of a subnormal operator Y remain true for tuples; e.g. the existence and uniqueness of its minimal normal extension N, the spectral inclusion σ(N)⊂ σ(Y)-proved for n-tuples in [4] and generalized to infinite tuples in [5]. However, neither the invariant subspace theorem nor the spectral mapping theorem in the “strong form” as in [3] is known so far for subnormal tuples. 
Rudol, K. The spectrum of orthogonal sums of subnormal pairs. Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 11-15. doi: 10.1017/S0017089500006984
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