Abstract
In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ALBRECHT, E.: On two questions of I. Colojoară and C. Foias. Manuscripta math.25, 1–15 (1978)
ALBRECHT, E. and FRUNZĂ, St.: Non-analytic functional calculi in several variables. Manuscripta math.18, 327–336 (1976)
ALBRECHT, E. and NEUMANN, M.: Automatische Stetigkeitseigenschaften einiger Klassen linearer Operatoren. Math. Ann.240, 251–280 (1979)
ALBRECHT, E.: Stetigkeitsaussagen für Homomorphismen zwischen topologischen Algebren. Preprint
ALBRECHT, E.: Local operators between spaces of ultradifferentiable functions and ultradistributions. Preprint
ALBRECHT, E. and VASILESCU, F.H.: Non-analytic local spectral properties in several variables. Czech. Math. J.24 (99), 430–443 (1974)
—: On spectral capacities. Rev. Roum. Math. Pures et Appl.19, 701–705 (1974)
APOSTOL, C.: Spectral decompositions and functional calculus. Rev. Roum. Math. Pures et Appl.13, 1481–1528 (1968)
BADĖ, W.G. and CURTIS, P.C.: Homomorphisms of commutative Banach algebras. Amer. J. Math.82, 589–608 (1960)
BADÉ, W.G., CURTIS, P.C. and LAURSEN, K.B.: Automatic continuity in algebras of differentiable functions. Math. Scand.40, 249–270 (1977)
CIORÁNESCU, J. and ZSIDÒ, L.: ω-ultradistributions and their applications in operator theory. INCREST Preprint series in Math.17 (1978)
COLOJOARĂ, I. and FOIAS, C.: Theory of generalized spectral operators. New York-London-Paris: Gordon and Breach 1968
DALES, H.G.: Automatic continuity: A survey. Bull. London Math. Soc.10, 129–183 (1978)
DE WILDE, M.: Closed graph theorems and webbed spaces. London-San Francisco-Melbourne: Pitman 1978
DUGUNDJI, J.: Topology. Boston: Allyn and Bacon 1966
FOIAS, C.: Spectral capacities and decomposable operators. Rev. Roum. Math. Pures et Appl.13, 1539–1545 (1968)
FRUNZĂ, St.: The Taylor spectrum and spectral decompositions. J. Functional Anal.19, 390–421 (1975)
JOHNSON, B.E.: Continuity of linear operators commuting with continuous linear operators. Trans. Amer. Math. Soc.128, 88–102 (1967)
JOHNSON, B.E. and SINCLAIR, A.M.: Continuity of linear operators commuting with continuous linear operators II. Trans. Amer. Math. Soc.146, 533–540 (1969)
KÖTHE, G.: Topological vector spaces II. New York-Heidelberg-Berlin: Springer 1979
PEETRE, J.: Rectification à l'article “Une caractérisation abstraite des opérateurs différentiels”. Math. Scand.8, 116–120 (1960)
RAIKOV, D.A.: Double closed-graph theorem for topological linear spaces. Siberian Math. J.7, 287–300 (1966)
SCHAEFER, H.H.: Topological vector spaces. New York-London: Macmillan 1966
SINCLAIR, A.M.: Automatic continuity of linear operators. Cambridge: Cambridge University Press 1976
TREVES, F.: Topological vector spaces, distributions and kernels. New York-London: Academic Press 1967
VRBOVÁ, P.: On continuity of linear transformations commuting with generalized scalar operators in Banach space. Časopis pro pěstování matematiky, Praha97, 142–150 (1972)
—: Structure of maximal spectral spaces of generalized scalar operators. Czech. Math. J.23, 493–496 (1973)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Albrecht, E., Neumann, M. Automatic continuity of generalized local linear operators. Manuscripta Math 32, 263–294 (1980). https://doi.org/10.1007/BF01299605
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01299605