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On Spaces of Compact Operators in Non-Archimedean Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Takemitsu Kiyosawa
Takemitsu Kiyosawa*
Affiliation:
Faculty of Education Shizuoka University Ohya, Shizuoka, 422 Japan
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Abstract

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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.

Keywords

46P0530G0512J25non-Archimedean Banach spacesspherically complete non-Archimedean valued fieldscompact operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 450 - 458
Copyright
Copyright © Canadian Mathematical Society 1989

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