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FK-multiplier spaces
Author(s):
D.
J.
Fleming;
J.
C.
Magee
Journal:
Proc. Amer. Math. Soc.
125
(1997),
175-181.
MSC (1991):
Primary 46A45
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Abstract:
In 1992 Grosse-Erdmann posed the problem of characterizing those FK-spaces containing the finitely nonzero sequences whose -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:
- 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
-dual of sequence spaces, Arch. Math. 58 (1992), 575-581. MR 93g:46008 - 8.
- J. C. Magee, The
-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
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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:
10.1090/S0002-9939-97-03620-4
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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