An Alternative to Plemelj-Smithies Formulas on Infinite Determinants

An alternative to Plemelj-Smithies formulas for the p-regularized quantities d(p)(K) and D(p)(K) is presented which generalizes previous expressions with p = 1 due to Grothendieck and Fredholm. Global upper bounds for these quantities are also presented. In particular, we prove that |d(p)(K)| ≤ eκ||K||pp holds with κ = κ(p) ≤ κ(∞) = e−1/4(1 + e2π) for p ≥ 3 which improves a previous estimate yielding κ(p) = e(2 + 1n(p − 1)).