Spectral manifolds for a class of operators
Daniel Kocan · Illinois Journal of Mathematics · 1966
KOCAN R(t) is an analytic function of on the open set p(T) and satisfies R(t) R() (t)R(t)R() [12,Th. 5. 1C].0.2.If T is closed nd p(T) is non-empty nd p() is ny polynomial then p(T) is closed operator [6, Th. 7, p. 602].0.3.If the polynomial p() is of degree nd if the vector x is in the domain of T nd is in p(T) then R()x is in the domain of T m+k nd p( T)R()mx R()p(T)x.In prticulr, R() commutes with ech power of T [6, Th. 8, p. 603].0.4.If T is closed, densely defined nd hs non-empty resolvent set p(T) then T is densely defined for ech positive integral m [6, Lemm 9, p. 648].1.1.We shM1 further ssume that the spectrum of T is on the rel xis nd that the resolvent operator R(z) stisfies the n-th order growth condition: [Imz[n[[R(z) K for 0 1