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On compact subsets in coechelon spaces of infinite order
Author(s):
Angela
A.
Albanese
Journal:
Proc. Amer. Math. Soc.
128
(2000),
583-588.
MSC (1991):
Primary 46A45;
Secondary 46A50
Posted:
July 6, 1999
MathSciNet review:
1625764
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Abstract:
For coechelon spaces  of infinite order it is proved that every compact subset of  is contained in a closed absolutely convex hull of some null sequence if and only if the matrix  is regularly decreasing.
References:
- [BMS]
- K. D. Bierstedt, R. Meise, W. Summers, Köthe sets and Köthe sequence spaces, pp. 27-91 in: ``Functional Analysis, Holomorphy and Approximation Theory'', North-Holland Math. Studies 71, Amsterdam 1982. MR 84f:46011
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- B. Cascales and J. Orihuela, Metrizability of precompact subsets in (LF)-spaces, Proc. Roy. Soc. Edinburgh 103A (1986), 293-299. MR 88b:46003
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- [DD2]
- S. Dierolf and P. Doma\'{n}ski, Null Sequences in Coechelon Spaces, Math. Nachr. 184 (1997), 167-176. MR 98a:46013
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- [D]
- P. Doma\'{n}ski, On Spaces of Continuous Functions with Values in Coechelon Spaces, to appear in Rev. Real Acad. Sci. Exactas, Madrid.
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- H. Neus, Über die Regularitätsbegriffe induktiver lokalkonvexer Sequenzen, Manuscripta Math. 25 (1978), 135-145. MR 58:2125
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- P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Math. Studies 131, Amsterdam 1987. MR 88j:46003
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Additional Information:
Angela
A.
Albanese
Affiliation:
Dipartimento di Matematica ``E. De Giorgi'', Università di Lecce, C.P. 193, Via per Arnesano, 73100, Lecce, Italy
Email:
albanese@ilenic.unile.it
DOI:
10.1090/S0002-9939-99-05039-X
PII:
S 0002-9939(99)05039-X
Keywords:
Compact set,
coechelon space of infinite order,
regularly decreasing
Received by editor(s):
August 12, 1997
Received by editor(s) in revised form:
April 14, 1998
Posted:
July 6, 1999
Additional Notes:
Research partially supported by the Italian MURST
Communicated by:
Dale Alspach
Copyright of article:
Copyright
1999,
American Mathematical Society
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