Document Zbl 0496.46006

On subseries convergent series and m-quasi-bases in topological linear spaces. (English) Zbl 0496.46006

Manuscr. Math. 38, 87-98 (1982).

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MSC:

46A35	Summability and bases in topological vector spaces
46B15	Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

Keywords:

quasi-basis; m-quasi-basis; subseries convergent series; topologically linearly independent; topologically linearly m-independent

Citations:

Zbl 0491.46005; Zbl 0159.416

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Full Text: DOI EuDML

References:

[1]	Bessaga, G., Peiczy?ski, A.: Selected topics in infinite-dimensional topology. Warsaw: Polish Scientific Publishers 1975 · Zbl 0304.57001
[2]	Christensen, J.P.R.: Compact convex sets and compact Choquet simpexes. Invent. Math. 19, 1-4 (1973) · Zbl 0247.46009 · doi:10.1007/BF01418847
[3]	Drewnowski, L.: Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodym theorems. Bull. Acad. Polon. Sei. Sér. Sci. Math. Astronom. Phys. 20, 725-731 (1972) · Zbl 0243.28011
[4]	? On minimally subspace-comparable F-spaees. J. Func. Anal. 26, 315-332 (1977) · Zbl 0366.46012 · doi:10.1016/0022-1236(77)90018-0
[5]	? Labuda, I., Lipecki, Z.: Existence of quasi-bases for separable topological linear spaces. Arch. Math. (Basel), 37, 454-456 (1981) · Zbl 0491.46005
[6]	Halmos, P.R.: A Hilbert space problem book. Toronto: Van Nostrand 1967 · Zbl 0144.38704
[7]	Klee, V.: On the borelian and projective types of linear subs-paces. Math. Seand. 6, 189-199 (1958) · Zbl 0088.08502
[8]	Kli?, C.: An example of noncomplete normed (K)-space. Bull. Aead. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26, 415-420 (1978) · Zbl 0393.46017
[9]	Labuda, I.: On the existence of non-trivial Saks sets and continuity of linear mappings acting on them. Ibid. 23, 885-890 (1975) · Zbl 0328.46017
[10]	Mackey, G.W.: On infinite-dimensional linear spaces. Trans. Amer. Math. Soc. 57, 155-207 (1945) · Zbl 0061.24301 · doi:10.1090/S0002-9947-1945-0012204-1
[11]	Peck, N.T.: On nonlocally convex spaces. II. Math. Ann 178, 209-218 (1968) · Zbl 0159.41601 · doi:10.1007/BF01350661
[12]	Popoola, J.O., Tweddle, I.: On the dimension of a complete metrizable topological vector space. Canad. Math. Bull. 20, 271-272 (1977) · Zbl 0359.46007 · doi:10.4153/CMB-1977-042-x
[13]	Rolewicz, S.: Metric linear spaces. Warsaw: Polish Scientific Publishers 1972 · Zbl 0226.46001
[14]	Singer, I.: Bases in Banach spaces. I. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0198.16601

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