GENERALIZED STOLZ MAPPINGS

In this paper, we introduce the class of generalized Stolz mappings. Also we prove that the class of $\ell ^{p}-$-type mappings is included in the class of generalized Stolz mappings and give a new quasinorm equivalent with $\Vert T\Vert_{\phi_{(p)}}$. Finally, we present some properties of the class of generalized Stolz mappings.

___

  • [1] A. Pietsch, Einigie neu Klassen von Kompakten linearen Abbildungen, revue Roum. Math. Pures et Appl., 8, 427-447, 1963.
  • [2] A. Pietsch, s-Numbers of operators in Banach spaces, Studia Mathematica, 51(3), 201-223,1974.
  • [3] B.Carl,A.Hinrichs, On s-numbers and Weyl inequalities of operators in Banach spaces, Bull.Lond. Math. Soc., 41(2), 332-340, 2009.
  • [4] B.Carl, On s-numbers,quasi s-numbers, s-moduli andWeyl inequalities of operators in Banach spaces, Rev. Mat. Complut., 23, 467-487, 2010.
  • [5] E. Evren Kara, Merve İlkhan, On a new class of s-type operators, Konuralp Journal of Mathematics, 3(1), 1-11, 2015
  • [6] G.Constantin, Operators of Ces-p-type, Rend. Accad.Naz.Lincei Sc. Fis. Mat.Nat., 52, 875-878, 1973
  • [7] I.Gohberg, M.Krein, Introduction to the theory of non-selfadjoint operators, A.M.S. Providence ,1969
  • [8] K.Iseki, A new class of mappings, Stolz mappings,Math.Japon., 3, 275-278, 1974.
  • [9] N.Tita, On Stolz mapping, Math.Japonica, 26(4), 495-496, 1981.
  • [10] N. Tita, Some interpolation properties and tensor product stability of Stolz mappings, International Conf. EITM European Integration Tradition and Modernity,\P. Maior" Univ., Tg. Mures, 666-669, 2007 (CD).
  • [11] N.Tita, On the approximation numbers of the tensor product operator, Analele Stuti ce ale Universitatii "al.I.Cuza" Iasi Tomul, XL,s.l.a., Matematicai, 1994.
  • [12] N.Tita, Some equivalent quasinorms on operator ideals, Spectral and Evolution Problems, Taurida National Univ. Simferopol, 13, 103-108, 2002.
  • [13] N. Tita, Operatori de clasa $\sigma _{p},$, Studii cercet. Mat.23, 467-487, 1971.
  • [14] N.Tita: On a class of $\ell _{\Phi ,\phi }$ operators, Collect. Mat. 32, 275-279, 1981.
  • [15] N. Tita, Ideale de operatori generate de s numere, Ed. Univ. Tranilvania, Brasov, 1998.
  • [16] N.Tita, Cuasinorme echivalente pe spatii de aproximare, Ed. Univ. Tranilvania, Brasov, 2001.
  • [17] N.Tita, A general view on approximation ideals, Functional Analysis and Applications, North Holland Mathematics Studies, 197, 295-300, 2004.
  • [18] Amit Maji, P.D. Srivastava, On operator ideals using weighted Cesaro sequence space, 22(3), 446-452, 2014.
  • [19] N.Salinas, Symmetric norm ideals and relative conjugate ideals,Trans. A.M.S., 188, 213-240, 1974.
  • [20] R. Schatten, Norm ideals of completely continuous operators, Springer Verlag, 1960.
  • [21] Bayram E., Wnuk W., Some Algebra Ideals Of Regular Operators, Commentationes Mathematicae, vol. 53, pp. 227233, 2013.