4. Let H be a Hilbert space. For any subset ACH (not only subspaces) we can define A = {t G H | Vu€ A: lu}. a (a) Show t

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4 Let H Be A Hilbert Space For Any Subset Ach Not Only Subspaces We Can Define A T G H Vu A Lu A A Show T 1 (19.56 KiB) Viewed 23 times

4. Let H be a Hilbert space. For any subset ACH (not only subspaces) we can define A = {t G H | Vu€ A: lu}. a (a) Show that A is a closed subspace of H. (b) Show that At = span(A)+, where span(A) C H denotes the linear span of A. (c) Let U CH be a subspace. Show that (Ut) is the closure of U. 5