Abstract
The definition of a spectral capacity has been proved to be a fruitful one in the theory of spectral decompositions of linear operators. Most of its standard properties still hold in the context of quotient Fréchet spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albrecht, E.; Vasilescu, F.-H.: On spectral capacities, Rev. Roumaine Math. Pures Appl.19 (1974), 701–705.
Apostol, C.: Spectral decompositions and functional calculus, Rev. Roumaine Math. Pures Appl.13 (1968), 1481–1528.
Colojoară, I.; Foiaş, C.: Theory of generalized spectral operators, Gordon and Breach, New York, 1968.
Dixmier, J.: Etude sur les variétés et les opérateurs de Julia, Bull. Soc. Math. France77 (1949), 11–101.
Douady, R.: Produits tensoriels topologiques et espaces nucléaires, Astérisque, Rev. Soc. Math. France, 1974, Exposé I.
Eschmeier, J.: Local properties of Taylor’s analytic functional calculus, Invent. Math.68 (1982), 103–116.
Eschmeier, J.: Analytische Dualität und Tensorprodukte in der meherdimensionalen Spektraltheorie, Habilitationsschrift, Münster, 1986.
Foiaş, C.: Spectral maximal spaces and decomposable operators in Banach spaces, Arch. Math.14 (1963), 341–349.
Foiaş, C.: Spectral capacities and decomposable operators, Rev. Roumaine Math. Pures Appl.13 (1968), 1539–1545.
Frunză, S.: The Taylor spectrum and spectral decompositions, J. Functional Analysis, 19 (1975), 390–421.
Godement, R.: Topologie algèbrique et théorie des faisceaux, Hermann, Paris, 1958.
Hörmander, L.: The analysis of linear partial differential operators I, Springer-Verlag, Berlin, 1983.
Putinar, M.: Spectral theory and sheaf theory I. Operator Theory: Advances and Applications Vol. 11, pp. 283–297, Birkhauser-Verlag, Basel, 1983.
Putinar, M.; Vasilescu, F.-H.: The local spectral theory needs Fréchet spaces, Preprint Series in Mathematics No. 16 (1982), INCREST, Bucureşti.
Radjabalipour, M.: On equivalence of decomposable and 2-decomposable operators, Pacific J. Math.77 (1978), 243–247.
Vasilescu, F.-H.: Analytic functional calculus and spectral decompositions, Editura Academiei and D. Reidel Publishing Company, Bucharest and Dordrecht, 1982.
Vasilescu, F.-H.: Analytic operators and spectral decompositions, Indiana Univ. Math. J.34 (1985), 705–722.
Vasilescu, F.-H.: Spectral theory in quotient Fréchet spaces I, Rev. Roumaine Math. Pures Appl.32 (1987), 561–579.
Vasilescu, F.-H.: Spectral theory in quotient Fréchet spaces II, Preprint, 1987.
Waelbroeck, L.: Le calcul symbolique dans les algèbres commutatives, J. Math. Pures Appl.33 (1954), 143–186.
Waelbroeck, L.: Quotient Fréchet spaces, Preprint, 1984, (to appear in: Rev. Roumaine Math. Pures Appl.).
Zhang Haitao: Generalized spectral decompositions (in Romanian), Dissertation, University of Bucharest, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to the memory of Constantin Apostol
Rights and permissions
Copyright information
© 1988 Springer Basel AG
About this chapter
Cite this chapter
Vasilescu, FH. (1988). Spectral Capacities in Quotient Fréchet Spaces. In: Gohberg, I. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5475-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-5475-7_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5477-1
Online ISBN: 978-3-0348-5475-7
eBook Packages: Springer Book Archive