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On inductive limits of Banach spaces. (English) Zbl 0327.46005


MSC:

46A08 Barrelled spaces, bornological spaces
46A20 Duality theory for topological vector spaces
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46B03 Isomorphic theory (including renorming) of Banach spaces
46B10 Duality and reflexivity in normed linear and Banach spaces

References:

[1] KÖTHE, G.: Topological Vector Spaces I, Berlin-Heidelberg-New York: Springer (1969). · Zbl 0179.17001
[2] PTÁK, V.: Completeness and the open mapping theorem. Bull. Soc. math France86, 41-74 (1958). · Zbl 0082.32502
[3] VALDIVIA, M.: A class of precompact sets in Banach spaces. J. reineangew. Math. (To appear). · Zbl 0306.46024
[4] VALDIVIA, M.: The space of distributions D?(?) is not Br-complete. Math. Ann. (To appear). · Zbl 0288.46033
[5] VALDIVIA, M.: Some examples on quasi-barrelled spaces. Ann. Inst. Fourier22, 21-26 (1972). · Zbl 0226.46005
[6] VALDIVIA, M.: On DF-spaces. Math. Ann. 191, 38-43 (1971). · Zbl 0204.12802 · doi:10.1007/BF01433469
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