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The spectrum of orthogonal sums of subnormal pairs

Published online by Cambridge University Press:  18 May 2009

K. Rudol
K. Rudol
Affiliation:
Instytut Matematyczny Pan, Kraków, ul. Solskiego 30, Poland
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 11 - 15
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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