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Math Help - Banach space proof

  1. #1
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    Banach space proof

    Let E & F be a Banach spaces .Then E X F is Banach space??
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  2. #2
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    That depends. If (u, v) is in E\times F, how do you define ||(u, v)||?
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  3. #3
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    The answer is yes, the product topology of ExF can be defined with a norm, for instance sup(|| ||_E,|| ||_F), or suming the norms , or taking the root of the sum of the squares of the norms. All the "natural norms" (l_1, l_2 or l_\infty type) are equivalent.
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