کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904683 | 1633754 | 2018 | 67 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Homogeneous families on trees and subsymmetric basic sequences
ترجمه فارسی عنوان
خانواده های همجنس درختان و توالی های پایه زیرمجموعه
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
We study density requirements on a given Banach space that guarantee the existence of subsymmetric basic sequences by extending Tsirelson's well-known space to larger index sets. We prove that for every cardinal κ smaller than the first Mahlo cardinal there is a reflexive Banach space of density κ without subsymmetric basic sequences. As for Tsirelson's space, our construction is based on the existence of a rich collection of homogeneous families on large index sets for which one can estimate the complexity on any given infinite set. This is used to describe detailedly the asymptotic structure of the spaces. The collections of families are of independent interest and their existence is proved inductively. The fundamental stepping up argument is the analysis of such collections of families on trees.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 334, 20 August 2018, Pages 322-388
Journal: Advances in Mathematics - Volume 334, 20 August 2018, Pages 322-388
نویسندگان
C. Brech, J. Lopez-Abad, S. Todorcevic,