Infinite Dimensional Linking

Martin Schechter

Chapter Chapter 5 in Critical Point Theory, 2020, pp 61-81 from Springer

Abstract: Abstract Let N be a closed, separable subspace of a Hilbert space E. |w We can define a new norm |v|w satisfying |v|w ≤∥v∥, ∀v ∈ N and such that the topology induced by this norm is equivalent to the weak topology of N on bounded subsets of N. This can be done as follows: Let {e k} be an orthonormal basis for N. Define ( u , v ) w = ∑ k = 1 ∞ ( u , e k ) ( v , e k ) 2 k , u , v ∈ N . $$\displaystyle (u,v)_w=\sum _{k=1}^{\infty }\frac {(u,e_k)(v, e_k)}{2^k}, \quad u,v\in N. $$

Date: 2020
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DOI: 10.1007/978-3-030-45603-0_5

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