#### 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 Technical Sciences, University "St. Kliment Ohridski" - Bitola,
Ivo Lola Ribar b.b., 7 000 Bitola, Macedonia

*e-mail:* `sonja.manchevska@uklo.edu.mk`
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.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.43.1.13

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