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Lorentz-Schatten Classes and Pointwise Domination of Matrices

Published online by Cambridge University Press:  20 November 2018

Fernando Cobos
Affiliation:
Departamento de Análisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid E-28040 Madrid Spain, email: cobos@eucmax.sim.ucm.es
Thomas Kühn
Affiliation:
Mathematisches Institut Universität Leipzig Augustusplatz 10/11 D-04109 Leipzig Germany, email: kuehn@mathematik.uni-leipzig.de
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Abstract

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We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Boas, R. P., Majorant problems for trigonometric series. J. Anal. Math. 10 (1962/63), 253271.Google Scholar
[2] Cobos, F. and Kühn, T., On a conjecture of Barry Simon on trace ideals. Duke Math. J. 59 (1989), 295299.Google Scholar
[3] Còrdoba, A., A counterexample in operator theory. Publ.Mat. 37 (1993), 335338.Google Scholar
[4] Déchamps-Gondim, M., Lust-Picard, F. and Queffelec, H., La proprieté du minorant dans C‘(H). C. R. Acad. Sci. Paris, Sér. I 295 (1982), 657659.Google Scholar
[5] Déchamps-Gondim, M., On the minorant properties in Cp(H). Pacific J. Math. 119 (1985), 89101.Google Scholar
[6] Gohberg, I. C. and Krein, M. G., Introduction to the Theory of Linear Nonselfadjoint Operators. Amer. Math. Soc., Providence, RI, 1969.Google Scholar
[7] König, H., Eigenvalue Distribution of Compact Operators. Birkhaüser, Basel, 1986.Google Scholar
[8] Peller, V. V., Hankel operators of class Sp and their applications (rational approximation, Gaussian processes, the problem of majorizing operators). Math. USSR-Sb. 41 (1982), 443479.Google Scholar
[9] Pietsch, A., Eigenvalues and s-numbers. Cambridge University Press, Cambridge, 1987.Google Scholar
[10] Simon, B., Trace Ideals and Their Applications. Cambridge University Press, Cambridge, 1979.Google Scholar
[11] Simon, B., Pointwise domination of matrices and comparison of Sp norms. Pacific J. Math. 97 (1981), 471475.Google Scholar