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Non-equivalent norms on C[0, 1].(a) Show that ∥f∥2 ≤ ∥f∥∞.(b) Find a sequence of functions (fN )satisfying ∥fN ∥2 N → ∞.(c) Show that ∥f∥1 ≤ ∥f∥2 (Hint:Cauchy-Schwarz).(d) Find a sequence of functions (fN )satisfying ∥fN ∥1N → ∞.

匿名用户 最后更新于 2021-12-01 19:08 数学类Mathematics

  1. Non-equivalent norms on C[0, 1].

    1. (a) Show that ∥f∥2 ≤ ∥f∥∞.

    2. (b) Find a sequence of functions (fN )satisfying ∥fN ∥2 N → ∞.

    3. (c) Show that ∥f∥1 ≤ ∥f∥2 (Hint:Cauchy-Schwarz).

    4. (d) Find a sequence of functions (fN )satisfying ∥fN ∥1

      N → ∞.PLEASE SOLVE JUST THE (D) PART

8. Non-equivalent norms on C[0, 1]. (a) Show that ||$||2 < || | ||00. (b) Find a sequence of functions (fn) satisfying ||fn||2 + 0 and ||fn|loo → o as N +0. (c) Show that || | ||1 = || F ||2 (Hint: Cauchy-Schwarz). (d) Find a sequence of functions (fn) satisfying ||fn||1 + 0 and 1 fn ||2 + oo as N +0.

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