Question

Show that the closed unit ball in a Hilbert space H is compact if and only...

Show that the closed unit ball in a Hilbert space H is compact if and only if H is finite dimensional. HINT: The closed unit ball must contain any basis.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
"The closed unit ball of an infinite-dimensional Banach space is not compact", why this does not...
"The closed unit ball of an infinite-dimensional Banach space is not compact", why this does not contradict Alaoglu's theorem?
Prove the the closed unit ball of an infinite dimensional Banach space is not compact (use...
Prove the the closed unit ball of an infinite dimensional Banach space is not compact (use Riesz's lemma). Comment on why this does not contradict Alaoglu's theorem.
Show that a compact subset of a Hausdorff space is closed in detail.
Show that a compact subset of a Hausdorff space is closed in detail.
Show that every orthonormal set in a Hilbert Space H is always linearly independent.
Show that every orthonormal set in a Hilbert Space H is always linearly independent.
Problem 6. For a closed convex nonempty subset K of a Hilbert space H and x...
Problem 6. For a closed convex nonempty subset K of a Hilbert space H and x ∈ H, denote by P x ∈ K a unique closest point to x among points in K, i.e. P x ∈ K such that ||P x − x|| ≤ ||y − x||, for all y ∈ K. First show that such point P x exists and unique. Next prove that all x, y ∈ H ||P x − P y|| ≤ ||x −...
Problem 3. Let S be a subspace of a Hilbert space H. Prove that (S⊥)⊥ is...
Problem 3. Let S be a subspace of a Hilbert space H. Prove that (S⊥)⊥ is the smallest closed subspace of H that contains S
if the state space s is finite, show that there must exist at least one closed...
if the state space s is finite, show that there must exist at least one closed communicating class. give an example of a transistion matrix with no such class
1. Suppose that ? is a finite dimensional vector space over R. Show that if ???(?...
1. Suppose that ? is a finite dimensional vector space over R. Show that if ???(? ) is odd, then every ? ∈ L(? ) has an eigenvalue. (Hint: use induction). (please provide a detailed proof) 2. Suppose that ? is a finite dimensional vector space over R and ? ∈ L(? ) has no eigenvalues. Prove that every ? -invariant subspace of ? has even dimension.
(2) If K is a subset of (X,d), show that K is compact if and only...
(2) If K is a subset of (X,d), show that K is compact if and only if every cover of K by relatively open subsets of K has a finite subcover.
What is the volume of the unit ball in R3 with coordinates (r, θ, h), where...
What is the volume of the unit ball in R3 with coordinates (r, θ, h), where x = r cos θ, y = r sin θ, z = h? Show your work and do not skip any steps. Then, find the volume of the unit ball in Rn, applying mathematical induction on n and the Fubini theorem.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT