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

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.

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  • [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.