PROPERTIES OF k th -ORDER (SLANT TOEPLITZ + SLANT HANKEL) OPERATORS ON H 2 (T)

摘要

For two essentially bounded Lebesgue measurable functions Φ and ξ on unit circle T, we attempt to study properties of operators S k M(Φ,ξ) = S k T Φ + S k H ξ on H 2 (T) (k ≥ 2), where S k T Φ is a k th -order slant Toeplitz operator with symbol Φ and S k H ξ is a k th -order slant Hankel operator with symbol ξ. The spectral properties of operators S k M(Φ,Φ) (or simply S k M(Φ) ) are investigated on H 2 (T). More precisely, it is proved that for k = 2, the Coburn’s type theorem holds for S k M(Φ) . The conditions under which operators S k M(Φ) commute are also explored.