Abstract
We characterize a nonlinear full invariant of compact Banach-space maps: Let (X, ‖.‖) and (Y, ‖.‖) be two Banach spaces and P C (X, Y) be all compact maps which map (X, ‖.‖) to (Y, ‖.‖). Then each weak operator-topology subseries-convergent series ∑ i P i in P c (X, Y) is also uniform-topology subseries-convergent iff each bounded map from (X, ‖.‖) to (l1, ‖.‖1) is a compact map. The necessary condition for each weak operator-topology subseries-convergent series ∑ i P i in P C (X, Y) to be also uniform-topology subseries-convergent is that (X, ‖.‖) and (X′, ‖.‖) both contain no copy of c0. This necessary condition is not sufficient.
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PACS: 02.10 By, 02.10 Gd
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Junde, W., Zhifeng, T. & Chengri, C. Nonlinear Full Invariant of Compact Banach-Space Maps. Int J Theor Phys 44, 277–282 (2005). https://doi.org/10.1007/s10773-005-2988-7
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DOI: https://doi.org/10.1007/s10773-005-2988-7