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Keywords:
vector-valued sequence space; topology; series; compact sets
vector-valued sequence space; topology; series; compact sets
Summary:
In this paper, a vector topology is introduced in the vector-valued sequence space $\text{\it BMC}\,(X)$ and convergence of sequences and sequentially compact sets in $\text{\it BMC}\,(X)$ are characterized.
References:
[1] Bu Q.Y.: Orlicz-Pettis type theorem for compact operators. Chinese Ann. of Math. 17A:1 (1996), 79-86. Zbl 0923.46007
[2] Li R.L., Bu Q.Y.: Locally convex spaces containing no copy of $c_0$. J. Math. Anal. Appl. 172:1 (1993), 205-211. MR 1199505
[3] Li R.L., Swartz C.: Spaces for which the uniform boundedness principle holds. Studia Sci. Math. Hungar. 27 (1992), 379-384. MR 1218160 | Zbl 0681.46001
[4] Pietsch A.: Nuclear Locally Convex Spaces. Springer-Verlag, Berlin, 1972. MR 0350360 | Zbl 0308.47024
[5] Wilansky A.: Modern Methods in Topological Vector Spaces. McGraw-Hill, New York, 1978. MR 0518316 | Zbl 0395.46001
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