Continuity of Multilinear Operator on Normed Linear Spaces
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Summary In this article, various definitions of contuity of multilinear operators on normed linear spaces are discussed in the Mizar formalism [4], [1] and [2]. In the first chapter, several basic theorems are prepared to handle the norm of the multilinear operator, and then it is formalized that the linear space of bounded multilinear operators is a complete Banach space. In the last chapter, the continuity of the multilinear operator on finite normed spaces is addressed. Especially, it is formalized that the continuity at the origin can be extended to the continuity at every point in its whole domain. We referred to [5], [11], [8], [9] in this formalization.
1964 ◽
Vol 60
(4)
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pp. 817-819
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2018 ◽
Vol 11
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pp. 740-750
2018 ◽
Vol 15
(01)
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pp. 65-83
1980 ◽
Vol 23
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pp. 347-354
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1971 ◽
Vol 12
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pp. 301-308
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2016 ◽
Vol 70
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pp. 19
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