Lorentz type spaces of ultrasmooth vectors of closed operators

  • M.I. Dmytryshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-3248-7736
  • O.V. Lopushansky University of Rzeszow, 1 Prof. St. Pigonia str., 35-310, Rzeszow, Poland
Published online: 2009-06-30

Abstract


Lorentz type spaces of ultrasmooth vectors of closed operators in Banach spaces are defined. Interpolation properties of such spaces are established and their application to the decision of problem of approaching of elements of Banach space is shown different classes of smooth vectors of the closed operator.