Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T13:08:55.699Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1.Conway, J. B., Subnormal operators, (Pitman Publishing Co., 1981).Google Scholar
2.Curto, R. E., Fredholm and invertible n-tuples of operators. The deformation problem. Trans. Amer. Math. Soc. 266 (1981) 129–159.Google Scholar
3.Dudziak, J., Spectral mapping theorems for subnormal operators, J. Functional Analysis 56 (1984), 360–387.CrossRefGoogle Scholar
4.Putinar, M., Spectral inclusion for subnormal n-tuples, Proc. Amer. Math. Soc. 90 (1984), 405–406.Google Scholar
5.Rudol, K., Extended spectrum of subnormal representations, Bull. Acad. Polon. Sci., Math. 31 (1983), 361–368.Google Scholar
6.Rudol, K., Spectral mapping theorems for analytic functional calculi, Operator Theory: Adv. Appl. 17 (1986), 331–340.Google Scholar
7.Sibony, N., Prolongement des fonctions holomorphes bornée et metrique de Carathéodory, Invent. Math. 29 (1975), 205–230.CrossRefGoogle Scholar
8.Taylor, J. L., A joint spectrum of several commuting operators, J. Functional Analysis 6 (1970), 1–38.CrossRefGoogle Scholar
9.Marchenko, A. V., Self-adjoint differential operators of an infinite number of variables, (in Russian) Mat. Sbornik (2) 96 (1975), 276–293.Google Scholar