I^*-Algebras and their Applications

抄録

We analyze the algebraic, topological, and order properties of I^*-algebras: complex unital topological *-algebras for which Σ_Jx_j^*x_j=0 implies x_j=0 (j∈J), J⊂N any finite subset. We consider the ergodic properties of states on an I^*-algebra with a distinguished group of automorphisms. Particular attention is given to I^*-algebras of the form E=Σ_N^⊕\bar{⊗}ⁿE where E is a nuclear LF-space. When E=\mathscr{S}(R⁴) (\mathscr{D}(R³)⊕\mathscr{D}(R³) respectively) then E has applications to relativistic quantum field theory (the canonical anti-commutation or commutation relations, respectively).