Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T20:23:54.500Z Has data issue: false hasContentIssue false
  • English
  • Français

On topological algebra sheaves

Part of: Analytic continuation Geometric convexity Genetics and population dynamics Methods of category theory in functional analysis

Published online by Cambridge University Press:  09 April 2009

Athanasios Kyriazis
Athanasios Kyriazis
Affiliation:
Department of Mathematics University of AthensPanepistimiopolis Athens 157 84, Greece
Rights & Permissions [Opens in a new window]

Abstract

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.

Given two topological algebra sheaves, we seek that their tensor product be an (algebra) sheaf of the same type. We further study the latter sheaf in connection with the set of morphisms which are defined on it. As an application, we finally consider fundamental notions and results related to algebras of holomorphic functions in the framework of topological algebra sheaves.

Keywords

Topological algebra sheaftopological geometric spacetensor product algebra sheafstructure sheaf envelopeDirac transformcentral morphism

MSC classification

Secondary: 46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) 46M05: Tensor products 32D10: Envelopes of holomorphy 32F99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 14 - 29
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Bourbaki, N., Algebra I, Chapters 1–3 (Addison-Wesley, Reading, 1974).Google Scholar
[2]Bredon, G. E., Sheaf theory (McGraw-Hill, New York, 1967).Google Scholar
[3]Bungart, L., ‘Holomorphic functions with values in locally convex spaces and applications to integral formulas’, Trans. Amer. Math. Soc. 111 (1964), 317–344.CrossRefGoogle Scholar
[4]Dowker, C. H., Lectures on sheaf theory (Tata Institute, Bombay, 1956).Google Scholar
[5]Dugundji, J., Topology (Allyn and Bacon, Boston, 1966).Google Scholar
[6]Gelbaum, B. R., ‘Tensor products over Banach algebras’, Trans. Amer. Math. Soc. 118 (1965), 525–547.CrossRefGoogle Scholar
[7]Godement, R., Théorie des faisceaux (Hermann, Paris, 1964).Google Scholar
[8]Grothendieck, A., Produits tensorielles topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (Amer. Math. Soc., Providence, 1955).Google Scholar
[9]Gunning, R. and Rossi, H., Analytic functions of several complex variables (Prentice-Hall, Englewood Cliffs, 1965).Google Scholar
[10]Harvey, R. and Wells, R. O. Jr, ‘Compact holomorphically convex subsets of a Stein manifold’, Trans. Amer. Math. Soc. 136 (1969), 509–516.CrossRefGoogle Scholar
[11]Horvath, J., Topological vector spaces and distributions (Addison-Wesley, Reading, 1966).Google Scholar
[12]Köthe, G., Topological vector spaces, II (Springer, Berlin, 1979).CrossRefGoogle Scholar
[13]Kultze, A., ‘Lokalholomorphe Funktionen und das Geschlecht kompakter Riemannschen Flächen’, Math. Ann. 143 (1961), 163–186.CrossRefGoogle Scholar
[14]Kyriazis, A., ‘On the spectra of topological A-tensor product A-algebras’, Yokohama Math. J. 31 (1983), 47–65.Google Scholar
[15]Kyriazis, A., ‘Tensor products of function algebras’, Bull. Austral. Math. Soc. 36 (1987), 417–423.CrossRefGoogle Scholar
[16]Kyriazis, A., ‘Direct limits and tensor products of topological A-algebras’, Mathematica Japonica 39 (1) (1994), 29–41.Google Scholar
[17]Kyriazis, A., ‘On central morphisms’, Bul. Greek Math. Soc., 34 (1992), 45–58.Google Scholar
[18]Kyriazis, A., ‘On tensor product α-algebra bundles’, in: Proc. Intern. Conf. Advances in the theory of Fréchet spaces, Istanbul, August, 1988, NATO ASI Series C 287 (Kluwer Academic Publishers, Dordrecht, 1989) pp. 223–234.Google Scholar
[19]Mallios, A., Topological algebras: Selected topics (North-Holland, Amsterdam, 1986).Google Scholar
[20]Mallios, A., ‘On topological algebra sheaves of a nuclear type’, Studia Math. 38 (1970), 215–220.CrossRefGoogle Scholar
[21]Mallios, A., ‘Topological algebras in several complex variables’, in: Proc. Intern. Conf. Funct. Anal. and Appl. Madras, 1973, Lecture Notes in Math. 399 (Springer, Berlin, 1974) pp. 342–377.Google Scholar
[22]Mallios, A., ‘Generalised structure sheaf envelopes of topological function algebra spaces’, Praktika Akad. Athēnōn 49 (1974), 373–385.Google Scholar
[23]Rickart, C. E., Holomorphic convexity for general function algebras (Yale University, Yale, 1967).Google Scholar
[24]Rickart, C. E., Natural function algebras (Springer, Berlin, 1979).CrossRefGoogle Scholar
[25]Tennison, B. R., Sheaf theory (Cambridge University Press, Cambridge, 1975).CrossRefGoogle Scholar