Hostname: page-component-77c89778f8-cnmwb Total loading time: 0 Render date: 2024-07-22T13:20:02.036Z Has data issue: false hasContentIssue false

Holomorphic Convexity for General Function Algebras

Published online by Cambridge University Press:  20 November 2018

C. E. Rickart*
Affiliation:
Yale University, New Haven, Conn.
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.

In previous papers (7; 8), we have investigated certain properties of general function algebras which may be regarded as generalizations or analogues of familiar results in the theory of analytic functions of several complex variables. This investigation is continued and expanded in the present paper. The main results concern a notion of holomorphic convexity for the general situation. We also extend somewhat several of the results obtained in the earlier papers.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

The research represented by this paper was partially supported by NSF Grant GP 5493.

References

1. Bochner, S. and Martin, W. T., Several complex variables (Princeton, 1948).Google Scholar
2. Glicksberg, I., Maximal algebras and a theorem ofRado, Pacific J. Math., 14 (1964), 919941.Google Scholar
3. Gunning, R. C. and Rossi, H., Analytic functions of several complex variables (Englewood Cliffs, N. J., 1965).Google Scholar
4. Kallin, Eva, A nonlocal function algebra, Proc. Nat. Acad. Sci. U.S.A., 49 (1963), 821824.Google Scholar
5. Quigley, F., Approximations by algebras of functions, Math. Ann., 135 (1958), 8192.Google Scholar
6. Rickart, C. E., General theory of Banach algebras (Princeton, 1960).Google Scholar
7. Rickart, C. E., Analytic phenomena in general function algebras, Pacific J. Math., 18 (1966), 361-377 ; Proc. Tulane Symposium on Function Algebras, edited by Birtel, F. (Chicago, 1966, pp. 6164.Google Scholar
8. Rickart, C. E., The maximal ideal space of functions locally approximable in a function algebra, Proc. Amer. Math. Soc, 17 (1966), 13201326.Google Scholar
9. Rossi, H., The local maximum modulus principle, Ann. of Math. (2), 72 (1960), 111.Google Scholar
10. Shauck, M. E., Algebras of holomorphic functions in ringed spaces, Ph.D. Dissertation, Tulane University, 1966.Google Scholar