摘要: For an operator T@?B(X,Y), we denote by a"m(T), c"m(T), d"m(T), and t"m(T) its approximation, Gelfand, Kolmogorov, absolute numbers, respectively. We show that, for any infinite-dimensional Banach spaces X Y, sequence @a"m@?0, there exists T@?B(X,Y) which the inequality 3@a"@?"m"/"6"@?>=a"m(T)>=max{c"m(t),d"m(T)}>=min{c"m(t),d"m(T)}>=t"m(T)>=@a"m/9 holds every m@?N. Similar results are obtained other s-scales.
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Bernard Maurey, Chapter 30 - Type, Cotype and K-Convexity Handbook of the Geometry of Banach Spaces. ,vol. 2, ,(2003) , 10.1016/S1874-5849(03)80037-2
Andrew Tonge, Hans Jarchow, Joseph Diestel, Absolutely summing operators ,(1995)
Albrecht Pietsch, Small ideals of operators Studia Mathematica. ,vol. 51, pp. 265- 267 ,(1974) , 10.4064/SM-51-3-265-267
Lior Tzafriri, Joram Lindenstrauss, Classical Banach spaces ,(1973)
Vicente Montesinos Santalucía, Václav Zizler, Jon Vanderwerff, Petr Hájek, Biorthogonal Systems in Banach Spaces ,(2007)
Israel Gohberg, M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators Published in <b>1969</b> in Providence RI) by American mathematical society. ,(1969)
Nicole Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals ,(1989)
William B. Johnson, Joram Lindenstrauss, Chapter 1 - Basic Concepts in the Geometry of Banach Spaces Handbook of the Geometry of Banach Spaces. ,vol. 1, pp. 1- 84 ,(2001) , 10.1016/S1874-5849(01)80003-6
Joram Lindenstrauss, W. B. Johnson, Handbook of the Geometry of Banach spaces Elsevier Science B.V.. ,vol. 2, ,(2001)
Asuman Güven Aksoy, Grzegorz Lewicki, Diagonal operators, s -numbers and Bernstein pairs Note di Matematica. ,vol. 17, pp. 209- 216 ,(1997) , 10.1285/I15900932V17P209