Quasi-affine transforms of subnormal operators

Che-Kao Fong

Vol. 70 (1977), No. 2, 361–368

DOI: 10.2140/pjm.1977.70.361

Abstract

For an operator T which is a quasi-affine transform of a subnormal operator S, we show that: (1) if S^∗ has no point spectrum and f : λ↦(T − λ)⁻¹x is defined on an open set Ω, then there is a dense subset Ω₀ of Ω such that f∣Ω₀ is analytic; and (2) if Σ is a spectral set of T and Q is a peak set of R(Σ), then the spectral manifold X_T(Q) is a reducing subspace of T and Q is a spectral set of T∣X_T(Q).

Mathematical Subject Classification 2000

Primary: 47B20

Milestones

Received: 14 September 1976

Revised: 14 September 1977

Published: 1 June 1977