ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM

Year 2017, Volume: 5 Issue: 2, 160 - 167, 15.10.2017

Abdelmoumen Tıaıba

Abstract

In this paper, we study a class of non commutative strongly $l_{p}$-summing sublinear operators and characterize this class of operators by given the extension of the Pietsch domination theorem. Some new properties are shown.

Keywords

Banach lattice, Completely bounded operator, Operator space, Strongly $l_{p}-$summing operator, Sublinear operator

References

• [1] D. Achour and L. Mezrag, Little Grothendieck's theorem for sublinear operators, J. Math. Anal. Appl. 296 (2004), 541-552.
• [2] D. Achour, L. Mezrag and A. Tiaiba, On the strongly $p$-summing sublinear operators,Taiwanesse J. Math. 11 (2007), no. 4, 969-973.
• [3] D. Blecher, The standard dual of an operator space, Pacic J. Math. 153 (1992), 15-30.
• [4] D. Blecher and V. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292.
• [5] J. S. Cohen, Absolutely p-summing, $p$-nuclear operators and their conjugates, Math. Ann. 201 (1973), 177-200.
• [6] E. Effros, Z. J. Ruan, A new approach to operator spaces, Canadian Math. Bull, 34 (1991), 329-337.
• [7] L. Mezrag, Comparison of non-commutative 2 and $p$-summing operators from B(l2) into OH, Zeitschrift fürr Analysis und ihre Anwendungen. Mathematical Analysis and its Applications 21 (2002), no. 3, 709-717.
• [8] L. Mezrag, On strongly $l_{p}$-summing m-linear operators, Colloquim Mathematicum, 111 (2008), no 1, 59-70.
• [9] G. Pisier, Non-commutative vector valued $L_{p}$-spaces and completely p-summing maps, Asterisque (Soc. Math. France) 247 (1998), 1-131.
• [10] G. Pisier, The operator Hilbert space OH, complex interpolation and tensor norms. Memoirs Amer. Math. Soc. 122, 585 (1996), 1-103.
• [11] A. Tiaiba, Characterization of $l_{p}$-summing sublinear operators, IAENG International Journal of Applied Mathematics, 39 (2009) no.4, 206-211.