Prove that the dual space of l^1 is l^infinity

Expert Solution

Do give a thumbs up if you like this solution

milcah answered 2 years ago

Prove the trace of an n x n matrix is an element of the dual space...

Prove the trace of an n x n matrix is an element of the dual space of all n x n matrices.

7. Show that the dual space H' of a Hilbert space H is a Hilbert space...

7. Show that the dual space H' of a Hilbert space H is a Hilbert space with inner product (', ')1 defined by (f .. fV)1 = (z, v)= (v, z), where f.(x) = (x, z), etc.

Let V be a finite-dimensional vector space over C and T in L(V). Prove that the...

Let V be a finite-dimensional vector space over C and T in L(V). Prove that the set of zeros of the minimal polynomial of T is exactly the same as the set of the eigenvalues of T.

prove that L^∞ is complete

1. Prove that any compact subset ot a metric space is closed and bounded. 2. Prove...

1. Prove that any compact subset ot a metric space is closed and bounded. 2. Prove that a closed subset of a compact set is a compact set.

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L...

1. Prove the language L is not regular, over the alphabet Σ = {a, b}. L = { aib2i : i > 0} 2) Prove the language M is not regular, over the alphabet Σ = {a, b}. M = { wwR : w is an element of Σ* i.e. w is any string, and wR means the string w written in reverse}. In other words, language M is even-length palindromes.

show x^1/3 is uniformly continuous on (-infinity,+infinity)

1. Let ? be a finite dimensional vector space with basis {?1,...,??} and ? ∈ L(?)....

1. Let ? be a finite dimensional vector space with basis {?1,...,??} and ? ∈ L(?). Show the following are equivalent: (a) The matrix for ? is upper triangular. (b) ?(??) ∈ Span(?1,...,??) for all ?. (c) Span(?1,...,??) is ?-invariant for all ?. please also explain for (a)->(b) why are all the c coefficients 0 for all i>k? and why T(vk) in the span of (v1,.....,vk)? i need help understanding this.

Prove the product of a compact space and a countably paracompact space is countably paracompact.

Prove that if the primal minimisation problem is unbounded then the dual maximisation problem is infeasible.

Question