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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

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.

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.

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

Abstract

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.
There are 11 citations in total.

Details

Subjects Engineering
Journal Section Research Article
Authors

Abdelmoumen Tıaıba This is me

Submission Date October 15, 2017
Acceptance Date May 31, 2017
Publication Date October 15, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Tıaıba, A. (2017). ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp Journal of Mathematics, 5(2), 160-167. https://izlik.org/JA67HA93UY
AMA 1.Tıaıba A. ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp J. Math. 2017;5(2):160-167. https://izlik.org/JA67HA93UY
Chicago Tıaıba, Abdelmoumen. 2017. “ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM”. Konuralp Journal of Mathematics 5 (2): 160-67. https://izlik.org/JA67HA93UY.
EndNote Tıaıba A (October 1, 2017) ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp Journal of Mathematics 5 2 160–167.
IEEE [1]A. Tıaıba, “ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM”, Konuralp J. Math., vol. 5, no. 2, pp. 160–167, Oct. 2017, [Online]. Available: https://izlik.org/JA67HA93UY
ISNAD Tıaıba, Abdelmoumen. “ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM”. Konuralp Journal of Mathematics 5/2 (October 1, 2017): 160-167. https://izlik.org/JA67HA93UY.
JAMA 1.Tıaıba A. ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp J. Math. 2017;5:160–167.
MLA Tıaıba, Abdelmoumen. “ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM”. Konuralp Journal of Mathematics, vol. 5, no. 2, Oct. 2017, pp. 160-7, https://izlik.org/JA67HA93UY.
Vancouver 1.Tıaıba A. ON A CLASS OF STRONGLY L$_{p}$-SUMMING SUBLINEAR OPERATORS AND THEIR PIETSCH DOMINATION THEOREM. Konuralp J. Math. [Internet]. 2017 Oct. 1;5(2):160-7. Available from: https://izlik.org/JA67HA93UY
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