ON A NEW CLASS OF s-TYPE OPERATORS

Year 2015, Volume: 3 Issue: 1, 1 - 11, 01.04.2015

Emrah Evren Kara Merve İlkhan

Abstract

In this paper, we introduce a new class of operators by using s-numbers and the sequence space Z(u; v; `p) for 1 < p < 1. We prove that this class is a quasi-Banach operator ideal. Also, we give some properties of the quasi-Banach operator ideal. Lastly, we establish some inclusion relations among the operator ideals formed by di erent s-number sequences.

Keywords

Operator ideals, s-numbers, quasi-norm, sequence spaces

References

• [1] B. Altay and F. Başar, Generalization of the sequence space `(p) derived by weighted mean, J. Math. Anal. Appl. Vol:330 (2007), 174-185.
• [2] J. Burgoyne, Denseness of the generalized eigenvectors of a discrete operator in a Banach space, J. Operator Theory Vol:33 (1995), 279-297.
• [3] Gh. Constantin, Operators of ces 􀀀 p type, Rend. Acc. Naz. Lincei. Vol:52 No.8 (1972), 875{878.
• [4] W. B. Johnson and J. Lindenstrauss, Handbook of the geometry of banach spaces, Elsevier Science B. V., North-Holand, 2001.
• [5] E. Kreyszig, Introductory functional analysis with applications, John Wiley Sons. Inc., The United States of America, 1978.
• [6] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxforf Vol:18 No.2 (1967), 345-355.
• [7] A. Maji and P. D. Srivastava, On operator ideals using weighted Cesaro sequence space, Egyp. Math. Soc., Vol:22 (2014), 446-452.
• [8] E. Malkowsky and E. Sava, Matrix transformations between sequence spaces of generalized weighted means, Appl. Math. Comp. Vol:147 (2004), 333-345.
• [9] A. Pietsch, Einige neue klassen von kompakten linearen Abbildungen, Rev. Math. Pures Appl. Vol:8 (1963), 427-447.
• [10] A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
• [11] A. Pietsch, s-numbers of operators in Banach spaces, Studia Math. Vol:51 (1974), 201-223.
• [12] A. Pietsch, Eigenvalues and s-numbers, Cambridge University Press, New York, 1986.
• [13] J. S. Shiue, On the Cesaro sequence spaces, Tamkang J. Math. Vol:1 No.1 (1970), 19-25.