Properties
- V is a bounded linear operator between Hilbert spaces, with Hermitian adjoint
- V is a Hilbert-Schmidt operator, hence in particular is compact.
- V has no eigenvalues and therefore, by the spectral theory of compact operators, its spectrum σ(V) = {0}.
- V is a quasinilpotent operator (that is, the spectral radius, ρ(V), is zero), but it is not nilpotent.
- The operator norm of V is exactly ||V|| = 2⁄π.
Read more about this topic: Volterra Operator
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—Ralph Waldo Emerson (1803–1882)
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—John Locke (1632–1704)