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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2002 • Question 5

Question

Math 6210 • Real Analysis 2002 • Question 5

Show that the parallelogram law fails for \(L^1([0,1])\) so it is not a Hilbert space.

Hint: Use \(f=\chi _{[0,1/2]}\) and \(g=\chi _{[1/2,1]}\).

Complex Analysis

Raw LaTeX

Show that the parallelogram law fails for \(L^1([0,1])\) so it is not
a Hilbert space.

Hint: Use \(f=\chi_{[0,1/2]}\) and \(g=\chi_{[1/2,1]}\).

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\textbf{Complex Analysis}
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Topic Tags

Fourier Analysis and Convolution Hilbert Spaces and Orthogonality Lp Spaces and Sequence Spaces