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2007, br. 30, str. 293-304
On orbits for pairs of operators on an infinite-dimensional complex Hilbert space
(naslov ne postoji na srpskom)
Faculty of Technical Sciences, Bitola, R. Macedonia

e-adresasonja.manchevska@uklo.edu.mk
Sažetak
(ne postoji na srpskom)
The results presented in this paper are motivated by some of the results obtained by B. Beauzamy in [1, Chap. III] for a single operator on an infinite-dimensional complex Hilbert space that imply existence of a dense set of vectors with orbits tending strongly to infinity. For the case of invertible operator T. one of B. Beauzamy's results implies that the space actually contains a dense set of vectors for which both the orbits under T and its inverse tend strongly to infinity. We are going to show that this is also true for any suitable pair of operators.
Reference
Beauzamy, B. (1988) Introduction to operator theory and invariant subspaces. Amsterdam: Elsevier Sci. Publ. B. V
Conway, J.B. (1985) A course in functional analysis. New York: Springer-Verlag
Mančevska, S. (2004) Operatori so orbiti što težat kon beskonečnost. u: 8th MSDR, Ohrid, str. 131-140
Miiller, V. (2001) Orbits, weak orbits and local capacity of operators. Int. Eq. Oper. Theory, 41, str. 230-253
Rudin, W. (1973) Functional analysis. New York, itd: McGraw-Hill
Rudin, W. (1974) Real and complex analysis. New York, itd: McGraw-Hill
van Neerven, J.M.A.M. (1995) On orbits of an operator with spectral radius one. Czech. Math. J., 45, str. 495-502
 

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jezik rada: engleski
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objavljen u SCIndeksu: 03.12.2007.

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