×

A note on the closed graph theorem. (English) Zbl 0351.46003


MSC:

46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
Full Text: DOI

References:

[1] M. M.Day, Normed Linear Spaces. Berlin 1973 · Zbl 0268.46013
[2] J. Dieudonné etL. Schwartz, La dualité dans les espaces (F) et (LF). Ann. Inst. Fourier Grenoble1, 61-101 (1950).
[3] M. De Wilde andC. Houet, On increasing sequences of absolutely convex sets in locally convex spaces. Math. Ann.192, 257-261 (1971). · doi:10.1007/BF02075355
[4] N. J. Kalton, Some forms of the closed graph theorem. Proc. Cambridge Philos. Soc.70, 401-408 (1971). · Zbl 0221.46006 · doi:10.1017/S0305004100050039
[5] G.Köthe, Topological Vector Spaces I. Berlin 1969. · Zbl 0179.17001
[6] M. Levin andS. Saxon, A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension. Proc. Amer. Math. Soc.29, 97-102 (1971). · Zbl 0212.14104 · doi:10.1090/S0002-9939-1971-0280973-2
[7] V. Pták, Completeness and the open mapping theorem. Bull. Soc. Math. France86, 41-74 (1958). · Zbl 0082.32502
[8] M. Valdivia, Some criteria for weak compactness. J. Reine Angew. Math.255, 165-169 (1972). · Zbl 0239.46001 · doi:10.1515/crll.1972.255.165
[9] M. Valdivia, A note on locally convex topologies. Math. Ann.201, 145-148 (1973). · Zbl 0252.46008 · doi:10.1007/BF01359791
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.