Abstract. A -semigroup on an infinite-dimensional separable complex Banach space is called subspace-hypercyclic for a subspace if is dense in for a vector . In this paper, we localize the notion of M-extended semigroup(resp. M-extended semigroup mixing) limit set of under and We give sufficient conditions of being -hypercyclic for this semigroup. Then by this result, we prove that is a -hypercyclic. This result is an answer of the question of B. F. Madore and R. A. Martnez-Avendano for -semigroup.

Received: June 12, 2016

Revised: September 3, 2016

Published: October 9, 2016

AMS Subject Classification: 47C03, 47A10, 47A11

Key Words and Phrases: -semigroup, subspace-hypercyclic, subspace-topologically transitive, class semigroup, class semigroup
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Bibliography

1

S.I. Ansari, Existance of hypercyclic operatos on topological vector space, J.F. Anal., 148 (1997), 384-390.

2

M.R. Azimi, V. Muller, A note on J-sets of linear operators, Revista de la Real Academia de Ciencias Exactass, Fisicas y Naturales, 105, No. 2 (2011), 449-453.

3

F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge University Press (2009).

4

N.P. Bhatia and G.P. Szeg, Stability Theory of Dynamical Systems, Die Grundlehren der mathematischen Wissenschaften, Band 161 Springer-Verlag, New York-Berlin (1970).

5

G. Costakis, A. Manoussos, J-class weighted shifts on the space of bounded sequences of complex numbers, Integral Equations Operator Theory, 62, No. 2 (2008), 149-158.

6

G. Costakis, A. Manoussos, J-class operators and hypercyclicity, J. Operator Theory, 67, No. 1 (2012), 101-119.

7

K.J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Grad. Texts in Math., vol. 194, Springer-Verlag, New York (2000).

8

K. Goswin and G. Erdmann, Universal families and hypercyclic operators, Bulletin of the American Mathematical Society, 35 (1999), 345-381.

9

R.R. Jiménez-Munguía, R.A. Martínez-Avendaño, A. Peris, Some questions about subspace hypercyclic operators, J. Math. Anal. Appl., 408 (2013), 209-212.

10

Karl-G. Grosse-Erdmann, Alfred Peris Manguillot, Linear Chaos, pringer-Verlag London Limited (2011).

11

C.M. Le, On Subspace-hypercyclicity operators, Proc. Amer. Math. Soc., 139, No. 8 (2011), 2847-2852.

12

F. Leon-Saavedra, V. Muller, Hypercyclic sequences of operators, Studia Math., 175, No. 1 (2006), 1-18.

13

B.F. Madore, R.A. Martínez-Avendano, Subspace hypercyclicity, J. Math. Anal. Appl., 373 (2011), 502-511.

14

A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci., vol. 44, Springer-Verlag, New York (1992).

15

H. Rezaei, Notes on subspace-hypercyclic operators, S.J. Math. Anal. Appl., 397 (2013), 428-433.

16

M.D. Rosa, C. Read, A hypercyclic operator whose direct sum is not hypercyclic, J. Operator Theory, 61 (2009), 369-380.

17

A. Tajmouati, A. El Bakkali, A. Toukmati, On M-hypercyclic semigroup, Int. J. Math. Anal., 9, No. 9 (2015) 417-428.

18

A. Tajmouati, M. El berrag, Some results on hypercyclicity of tuple of operators, Italian Journal of Pure and Applied Mathematics, 35 (2015), 487-492.

19

S. Talebi, M. Asadipour, On subspace-transitive operators, Int. J. of Pure and Appl. Math., 84, No. 5 (2013), 643-649.

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DOI: 10.12732/ijpam.v109i4.9 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: 109
Issue: 4
Pages: 861 - 868

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