IJPAM: Volume 110, No. 4 (2016)

Title

ORBIT OF TUPLE OF OPERATORS TENDING TO INFINITY

Authors

Abdelaziz Tajmouati$^1$, Youness Zahouan$^2$
$^{1,2}$Laboratory of Mathematical Analysis and Applications
Faculty of Sciences Dhar Al Mahraz
Sidi Mohammed Ben Abdellah University
Fez, MOROCCO

Abstract

In this paper we prove that there is a dense set of vectors in $X$ whose orbits under the tuple $\mathcal{T} = (T_{1} , T_{2} ,..., T_{n})$ of commutative bounded linear operators on a infinite dimensional (real, complex) Banach space $X$ tend to infinity.

History

Received: August 17, 2016
Revised: October 4, 2016
Published: November 9, 2016

AMS Classification, Key Words

AMS Subject Classification:
Key Words and Phrases: tuple of operators, orbit, spectral radius, spectrum, point spectrum, approximate point spectrum, bounded below operator

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Bibliography

1
S. Mancevska, M. Orovcanec, Orbits tending srongly to infinity under pairs of operators on reflexive Banach spaces, Glasnik Matematicki, 43, No. 63 (2008), 195-204.

2
S. Mancevskaw, M. Orovcanec, orbits tending to infinity under sequences of operators on Banach spaces, Glasnik Matematicki, 47, No. 2 (2008), 175-183.

3
S. Mancevska, On orbits for pairs of operators on an infinite-dimensional complex Hilbert space, Kragujevac J. Math., 30 (2007), 293-304.

4
S. Mancevska, M. Orovcanec, Orbits tending to infinity under sequences of operators on Hilbert spaces, Filomat, 21, No. 2 (2007), 161-171.

5
V. Muller, J. Vrsovsky, Orbits of linear operators tending to infinity, Rocky Mountain J. Math., 39, No. 1 (2009), 219-230.

6
V.Muller, Weak orbits and a local capacity of operators, Int. Eq. Oper. Theory, 41 (2001), 230-253.

7
N.S. Feldman, Hypercyclic tuples of operators and somewhere dense orbits, J. Math. Appl., 346 (2008), 82-98.

8
B. Yousefi, Gh.R. Moghimi, On the hypercyclicity for a tuple of operator, 76, No. 2 (2012), 261-265

9
B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North Holland, 1988.

10
A.L. Shields, Weighted shift operators and analytic function theory, In: Topics in Operator Theory, Mathematical Surveys, No. 13 (Ed. C. Pearsy), 49-128, American Math. Soc., Providence, Rhode Island, 1974.

How to Cite?

DOI: 10.12732/ijpam.v110i4.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 110
Issue: 4
Pages: 651 - 656


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