Asymmetric Putnam-Fuglede Theorem for (n, k)-Quasi-*-Paranormal Operators

Bachir, Ahmed ✉; Segres, Abdelkader

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: SYMMETRY 2073-8994 11 (1) Paper: 64 , 14 p. 2019
  • SJR Scopus - Computer Science (miscellaneous): Q2
Azonosítók
Szakterületek:
    T is an element of B(H) is said to be (n, k)-quasi-*-paranormal operator if, for non-negative integers k and n, parallel to T*(T(k)x)parallel to((1 + n)) <= T(1 + n)(T(k)x)parallel to parallel to T(k)x parallel to(n); for all x is an element of H. In this paper, the asymmetric Putnam-Fuglede theorem for the pair (A, B) of power-bounded operators is proved when (i) A and B* are n-*-paranormal operators (ii) A is a (n, k)-quasi-*-paranormal operator with reduced kernel and B is n-*-paranormal operator. The class of (n, k)-quasi-*-paranormal operators properly contains the classes of n-*-paranormal operators, (1, k)-quasi-*-paranormal operators and k-quasi-*-class A operators. As a consequence, it is showed that if T is a completely non-normal (n, k)-quasi-*-paranormal operator for k = 0, 1 such that the defect operator DT is Hilbert-Schmidt class, then T is an element of C-10.
    Hivatkozás stílusok: IEEEACMAPAChicagoHarvardCSLMásolásNyomtatás
    2021-10-25 00:56