Existence and uniqueness of physical ground states

AbstractIt is proved that if A is a bounded Hermitian operator on a probability Hilbert algebra which preserves positivity and is continuous from L2 to Lp for some p > 2 then ∥ A ∥ is an eigenvalue of A. A sufficient condition is given for its multiplicity to be one. Applications are given to the proof of existence and nondegeneracy of physical ground states in quantum field theory for physical systems involving Fermions or Bosons