Academic Journal
CLASSES OF STRICTLY SINGULAR OPERATORS AND THEIR PRODUCTS
| العنوان: | CLASSES OF STRICTLY SINGULAR OPERATORS AND THEIR PRODUCTS |
|---|---|
| المؤلفون: | George Androulakis, Gleb Sirotkin, Vladimir, G. Troitsky |
| المساهمون: | The Pennsylvania State University CiteSeerX Archives |
| المصدر: | http://arxiv.org/pdf/math/0609039v1.pdf. |
| سنة النشر: | 2006 |
| المجموعة: | CiteSeerX |
| الوصف: | V. D. Milman proved in [14] that the product of two strictly singular operators on Lp[0, 1] (1 � p < ∞) or on C[0, 1] is compact. In this note we utilize Schreier families Sξ in order to define the class of Sξ-strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this class are compact, under the assumption that the underlying Banach space has finitely many equivalence classes of Schreier-spreading sequences. Finally we define the class of Sξ-hereditarily indecomposable Banach spaces and we examine the operators on them. 1. Classes of strictly singular operators Recall that a bounded operator T from a Banach space X to a Banach space Y is called strictly singular if its restriction to any infinite-dimensional subspace is not an isomorphism. That is, for every infinite dimensional subspace Z of X and for every ε> 0 there exists z ∈ Z such that ‖Tz ‖ < ε‖z‖. We say that T is finitely strictly singular if for every ε> 0 there exists n ∈ N such that for every subspace Z of X with dim Z � n there exists z ∈ Z such that ‖Tz ‖ < ε‖z‖. In particular, for |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.8119; http://arxiv.org/pdf/math/0609039v1.pdf |
| الاتاحة: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.8119 http://arxiv.org/pdf/math/0609039v1.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| رقم الانضمام: | edsbas.E3A97C2D |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |