IJPAM: Volume 63, No. 3 (2010)

MODULUS HYPERINVARIANT CLOSED IDEALS FOR
QUASINILPOTENT OPERATORS WITH MODULUS
ON $l_p$-SPACES

Mingxue Liu
Department of Mathematics
Guangdong Polytechnic Normal University
Guangzhou, 510665, P.R. CHINA
e-mail: [email protected]


Abstract.In this paper, it is proved that every non-zero continuous operator with modulus on an $l_p$-space whose modulus is quasinilpotent at a non-zero positive vector has a non-trivial modulus hyperinvariant closed ideal.

Received: July 11, 2010

AMS Subject Classification: 47A15

Key Words and Phrases: $l_p$-space, quasinilpotent operator, invariant subspace, invariant ideal

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3