Abstract
The tensor structure of spaces L p (R n) of summable functions of several variables is described. A scale of Hardy-type spaces of analytic functionals defined in the unit ball of the space L p (R 1) of summable functions of one variable is introduced. One-parameter groups of isometries of such spaces of analytic functionals are investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Ya. Helemsky, Homologies in Banach and Topological Algebras [in Russian], Moscow State University, Moscow (1986).
H. H. Schaefer, Topological Vector Spaces, Macmillan, New York (1966).
R. M. Aron, B. J. Cole, and T. W. Gamelin, “Spectra of algebras of analytic functions on a Banach space, ” J. Reine Angew. Math., 415, 51–93 (1991).
T. K. Carne, B. J. Cole, and T. W. Gamelin, “A uniform algebra of analytic functions on a Banach space, ” Trans. Amer. Math. Soc., 314, 639–659 (1989).
S. Dineen, Complex Analysis in Locally Convex Spaces, Math. Studies, Vol. 57, North-Holland, Amsterdam (1981).
T. W. Gamelin, Analytic Functions on Banach Space, Complex Function Theory (Gauthier and Sabidussi, eds.), Kluwer Academic Publishers (to appear).
A. Grothendieck, “Produits tensoriel topologues et espases nucleaire,” Mem. Amer. Math. Soc., 16, No. 2, 1–140 (1955).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Academic Press (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lopushansky, O.V., Zagorodnyuk, A.V. Groups of Isometries of Hardy-Type Spaces of Analytic Functionals in the Unit Ball of the Space~L p . Journal of Mathematical Sciences 107, 3570–3576 (2001). https://doi.org/10.1023/A:1011938106204
Issue Date:
DOI: https://doi.org/10.1023/A:1011938106204