On Hilbert-Schmidt Tuples of Commutative Bounded Linear Operators on
Separable Banach Spaces

Mezban Habibi

doi:https://doi.org/10.14445/22315373/IJMTT-V8P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 8 | Number 2 | Year 2014 | Article Id. IJMTT-V8P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V8P514

On Hilbert-Schmidt Tuples of Commutative Bounded Linear Operators on Separable Banach Spaces

Mezban Habibi

Citation :

Mezban Habibi, "On Hilbert-Schmidt Tuples of Commutative Bounded Linear Operators on Separable Banach Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 8, no. 2, pp. 103-111, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V8P514

Abstract

In this paper, we will study some properties of Tuples that there components are commutative bounded linear operators on a separable Hilbert space H, then we will develop those properties for infinity-Tuples and find some conditions for them to be Hilbert-Schmidt infinity tuple. The infinity-Tuples is called Hilbert-Schmidt infinity tuple if for every orthonormal basis {µi} and {λi} in H we have had Calculation of doing by supreme over i for i=1, 2, 3...

Keywords

Hypercyclic vector, Hypercyclicity Criterion, Hilbert-Schmidt, Infinity -tuple, Periodic point.

References

[1] J. Bes, Three problems on hypercyclic operators, PhD thesis, Kent State University, 1998.
[2] P. S. Bourdon and J. H. Shapiro, Cyclic Phenomena for Composition Operators, Memoirs of Amer. Math. Soc. (125), Amer. Math. Providence, RI, 1997.
[3] R. M. Gethner and J. H. Shapiro, Universal vectors for Operators on Spaces of Holomorphic Functions, Proc. Amer. Math. Soc., (100) (1987), 281-288.
[4] G. Godefroy and J. H. Shapiro, Operators with dense, Invariant, Cyclic vector manifolds, J. Func. Anal., 98 (2) (1991), 229-269.
[5] K. Goswin and G. Erdmann, Universal Families and Hypercyclic Operators, Bulletin of the American Mathematical Society, 98 (1991), 229-269.
[6] M. Habibi, n-Tuples and Chaoticity, Int. Journal of Math. Analysis, 6 (14) (2012), 651-657.
[7] M. Habibi, ∞-Tuples of Bounded Linear Operators on Banach Space, Int. Math. Forum, 7 (18) (2012), 861-866.
[8] M. Habibi and B. Yousefi, Conditions for a Tuple of Operators to be Topologically Mixing, Int. Jour. App. Math., 23 (6) (2010), 973-976.
[9] C. Kitai, Invariant closed sets for linear operators, Thesis, University of Toronto, 1982.
[10] A. Peris and L. Saldivia, Syndentically hypercyclic operators, Integral Equations Operator Theory, 5 (2) (2005), 275-281.
[11] S. Rolewicz, On orbits of elements, Studia Math., (32) (1969), 17-22.
[12] H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc., (347) (1995), 993-1004.
[13] G. R. McLane, Sequences of derivatives and normal families, Jour. Anal. Math., 2 (1952), 72-87.
[14] B. Yousefi and M. Habibi, Hypercyclicity Criterion for a Pair of Weighted Composition Operators, Int. Jour. of App. Math., 24, (2) (2011), 215-219.
[15] B. Yousefi and M. Habibi, Syndetically Hypercyclic Pairs, Int. Math. Forum, 5(66) (2010), 3267-3272.