Glasnik Matematicki, Vol. 43, No.1 (2008), 195-204.

ORBITS TENDING STRONGLY TO INFINITY UNDER PAIRS OF OPERATORS ON REFLEXIVE BANACH SPACES

Sonja Mančevska and Marija Orovčanec

Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Ss. Ciryl and Methodius University - Skopje, Gazi Baba b.b., P.O. BOX 162, 1 000 Skopje, Macedonia
e-mail: marijaor@iunona.pmf.ukim.edu.mk

Abstract.   In our previous paper, we gave some sufficient conditions under which, for given pair of bounded linear operators T and S on an infinite-dimensional complex Hilbert space H, there is a dense set of vectors in H with orbits under T and S tending strongly to infinity. In this paper we are going to extend these results for pairs of operators on an infinite-dimensional complex and reflexive Banach space.

2000 Mathematics Subject Classification.   47A05, 47A25, 47A60.

Key words and phrases.   Approximate point spectrum, bounded linear operators, orbits tending strongly to infinity, reflexive Banach space.

DOI: 10.3336/gm.43.1.13

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