Name: Hoda
Question: In the book "Linear Functional Analysis" from Epstein there is a proof (page 116) of the following theorem: The dual space of L^{p} is equal to L^{q}. Later, it is stated as a theorem without proof that for 1 <= p < +infinite, The dual space of l^{p} is equal to l^{q}. I would like to prove this later theorem. I am able to find a member of the dual space of l^{p} for each member of l^{q}, namely Let b = (b1, b2, b3, ...) be any member of l^{q}; and let a = (a1, a2, a3, ...) be a member of l^{p}. then the linear functional defined as my_l(a) = Sum of the infinite series a1+b1, a2+b2, a3+b3, ... is a bounded linear functional on l^{p} (that is, belongs to the dual space of l^{p}). Moreover, this correspondence between (l^{p})* and l^{q} is normpreserving. Now, given a member l of the dual space of l^{p}, I need to find a member b of l^{q} such that l = my_l. Could you please help me to finish this proof or point me to a book where I could find the solution? Thanks a lot in advance, Hi Hoda,Several books have this result. For example, Page 143 of A.E. Taylor and D.C. Lay, Introduction to Functional Analysis, 2nd Edition, John Wiley & Sons, 1980. Doug
