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

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milcah answered 2 years ago

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.

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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.

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

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