Linear Operators: Spectral operators

adjoint operator algebra Amer analytic applications arbitrary B-space Banach Banach space belongs Boolean algebra Borel sets bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator Doklady Akad domain elements equation equivalent established example exists extension finite follows formula function given gives Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math Moreover multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero