Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

FK-multiplier spaces


Authors: D. J. Fleming and J. C. Magee
Journal: Proc. Amer. Math. Soc. 125 (1997), 175-181
MSC (1991): Primary 46A45
DOI: https://doi.org/10.1090/S0002-9939-97-03620-4
MathSciNet review: 1353384
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In 1992 Grosse-Erdmann posed the problem of characterizing
those FK-spaces containing the finitely nonzero sequences whose $\beta $-duals are themselves FK. Here we consider the more general problem of characterizing FK-spaces containing the finitely nonzero sequences with the property that the multipliers into a BK-sum space admit an FK-topology.


References [Enhancements On Off] (What's this?)

  • 1. M. Benholz, Faktorfolgenräume und ihre LFK-Topologien, Dissertation, Fernuniversität, Hagen (1993).
  • 2. M. Buntinas, On Toeplitz sections in sequences spaces, Math. Proc. Camb. Phil. Soc. 78 (1975), 451-460. MR 53:13913
  • 3. -, Products of sequence spaces, Analysis 7 (1987), 293-304. MR 89f:46017
  • 4. M. Buntinas and G. Goes, Products of sequences spaces and multipliers, Radovi Matemati[??]cki 3 (1987), 287-300. MR 89f:46017
  • 5. L. Crone, D. J. Fleming, and P. Jessup, Diagonal nuclear operators, Studia Math. 43 (1972), 51-56. MR 48:837
  • 6. D. J. Fleming, Unconditional Toeplitz sections in sequence spaces, Math. Z. 194 (1987), 405-414. MR 88h:46010
  • 7. K. G. Grosse-Erdmann, On the $f$-dual of sequence spaces, Arch. Math. 58 (1992), 575-581. MR 93g:46008
  • 8. J. C. Magee, The $\beta $-dual of FK-spaces, Analysis 8 (1988), 25-32. MR 89j:46009
  • 9. R. J. McGivney and W. Ruckle, Multipler algebras of biorthogonal systems, Pacific J. Math. 29 (1969), 375-387. MR 54:3358
  • 10. W. H. Ruckle, An abstract concept of the sum of a numerical series, Can. J. Math. 22 (1970), 863-874. MR 42:3463
  • 11. -, A universal topology for sequence spaces, Math. Ann. 236 (1978), 43-48. MR 58:2153
  • 12. -, Representation and series summability of complete biorthogonal sequences, Pacific J. Math. 34 (1970), 511-528. MR 42:2219
  • 13. -, Topologies on sequence spaces, Pacific J. Math. 42 (1972), 235-249. MR 47:7384
  • 14. -, Sequence spaces, Pitman, London, 1981. MR 83g:46012
  • 15. A. Wilansky, Summability through functional analysis, North-Holland, Amsterdam, 1984. MR 85d:40006
  • 16. K. Zeller, Allgemeine eigenschaften von limitierungsverfahren, Math. Z. 53 (1951), 463-487. MR 12:604e

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46A45

Retrieve articles in all journals with MSC (1991): 46A45


Additional Information

D. J. Fleming
Affiliation: Department of Mathematics, St. Lawrence University, Canton, New York 13617

J. C. Magee
Affiliation: Department of Mathematics, SUNY at Potsdam, Potsdam, New York 13676

DOI: https://doi.org/10.1090/S0002-9939-97-03620-4
Keywords: FK-space, multiplier space, sum space
Received by editor(s): June 24, 1995
Received by editor(s) in revised form: July 7, 1995
Communicated by: Dale Alspach
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society