IJPAM: Volume 63, No. 3 (2010)
MODULUS HYPERINVARIANT CLOSED IDEALS FOR
QUASINILPOTENT OPERATORS WITH MODULUS
ON
-SPACES
QUASINILPOTENT OPERATORS WITH MODULUS
ON
-SPACES
Mingxue Liu
Department of Mathematics
Guangdong Polytechnic Normal University
Guangzhou, 510665, P.R. CHINA
e-mail: liumingxue9698@sina.com.cn
Department of Mathematics
Guangdong Polytechnic Normal University
Guangzhou, 510665, P.R. CHINA
e-mail: liumingxue9698@sina.com.cn
Abstract.In this paper, it is proved that every non-zero continuous operator with modulus on an -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: -space, quasinilpotent operator, invariant subspace, invariant ideal
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3