Geodesic
On Spaces of Compact Operators in Non-Archimedean Banach Spaces
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 450-458

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DOI

Let K be a non-trivial complete non-Archimedean valued field and let E be an infinite-dimensional Banach space over K. Some of the main results are:(1) K is spherically complete if and only if every weakly convergent sequence in l∞ is norm-convergent.(2) If the valuation of K is dense, then C0 is complemented in E if and only if C(E,c0) is n o t complemented in L(E,c0), where L(E,c0) is the space of all continuous linear operators from E to c0 and C(E,c0) is the subspace of L(E, c0) consisting of all compact linear operators.
DOI : 10.4153/CMB-1989-065-x
Mots-clés : 46P05, 30G05, 12J25, non-Archimedean Banach spaces, spherically complete non-Archimedean valued fields, compact operators 
Kiyosawa, Takemitsu. On Spaces of Compact Operators in Non-Archimedean Banach Spaces. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 450-458. doi: 10.4153/CMB-1989-065-x
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     title = {On {Spaces} of {Compact} {Operators} in {Non-Archimedean} {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {450--458},
     year = {1989},
     volume = {32},
     number = {4},
     doi = {10.4153/CMB-1989-065-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-065-x/}
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