Everything is in the title I guess. Maybe is the scalar product that defines orthogonality continuous? But why would it be?
Clément
Why is the orthogonal complement of a subset of an Hilbert space always equal to the orthogonal complement of the closure of the subset?
0
$\begingroup$
linear-algebra
-
1Yes, it is continuous. Hint: Cauchy-Schwarz. – 2017-02-23
1 Answers
0
A scalar product is continuous with respect to the norm it induces in virtue of the Cauchy-Schwarz inequality.