On the topology of the space of convolution operators in
Author:
Saleh Abdullah
Journal:
Proc. Amer. Math. Soc. 110 (1990), 177-185
MSC:
Primary 46F05; Secondary 46F10
DOI:
https://doi.org/10.1090/S0002-9939-1990-1017842-8
MathSciNet review:
1017842
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we show that on the space of convolution operators on
, the topology
of uniform convergence on bounded subsets of
is equal to the strong dual topology.
- [1] Saleh Abdullah, On distributions of rapid growth, Portugal. Math. 47 (1990), no. 2, 191–204. MR 1090070
- [2] Saleh Abdullah, On the spaces of convolution operators and multipliers in 𝒦’_{ℳ}, J. Univ. Kuwait Sci. 15 (1988), no. 2, 219–228 (English, with Arabic summary). MR 974040
- [3] Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062
- [4] G. Sampson and Z. Zieleźny, Hypoelliptic convolution equations in 𝐾′_{𝑝}, 𝑝>1, Trans. Amer. Math. Soc. 223 (1976), 133–154. MR 425607, https://doi.org/10.1090/S0002-9947-1976-0425607-8
- [5] Helmut H. Schaefer, Topological vector spaces, Springer-Verlag, New York-Berlin, 1971. Third printing corrected; Graduate Texts in Mathematics, Vol. 3. MR 0342978
- [6] Z. Zieleźny, On the space of convolution operators in \cal𝐾₁′, Studia Math. 31 (1968), 111–124. MR 248520, https://doi.org/10.4064/sm-31-2-111-124
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46F05, 46F10
Retrieve articles in all journals with MSC: 46F05, 46F10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-1017842-8
Article copyright:
© Copyright 1990
American Mathematical Society