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Optimal weyl inquality in banach spaces

Dedicated to Professor Albrecht Pietsch on the occasion of his 70th birthday A well-known multiplicative Weyl inequality states that the sequence of eigenvalues (λ k (T)) and the sequence of approximation numbers (a k (T)) of any compact operator T in a Banach space satisfy |λ k (T)| ≤ n n/2 a k (T) for all n. We prove here that the constant n n/2 is optimal, which solves a longstanding problem.