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On the Distance between an Operator and an Ideal

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Recent Advances in Operator Theory, Operator Algebras, and their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 153))

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Abstract

Let L(X) be the normed algebra of all bounded linear operators T : X → X, where X is a normed space, and let I be an operator ideal, so that I(X) is a two-sided ideal in L(X). If X is a tensor product of normed spaces, endowed with a tensor norm, an estimation is given for the distance of a tensor product operator T ЄL(X) to I(X) and it is applied to the study of the quasi-nilpotency of tensor product operators modulo I(X).

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University Transilvania of Braşov, Braşov, România

    Nicolae Tiţa

Authors
  1. Nicolae Tiţa
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of the West Timişoara, Bul. V. Parvan Nr. 4, 1900, Timişoara, Romania

    Dumitru Gaşpar

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest, 70700, Romania

    Dan Timotin

  3. Dipartimento di Matematica, Università di Roma „Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    László Zsidó

  4. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  5. Laboratoire AGAT-UMR 8524 U.F.R. de mathématiques, Université des Sciences et Technologie de Lille, 59655, Villeneuve d’Ascq Cedex, France

    Florian-Horia Vasilescu

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© 2004 Birkhäuser Verlag Basel/Switzerland

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Tiţa, N. (2004). On the Distance between an Operator and an Ideal. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_17

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