Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
The definition that I am using for subsymmetric sequence requires the sequence to be unconditional. Under this definition, is a subsymmetric sequence always bounded away from zero? Do you know/have a reference/hint related to the dichotomy for subsymmetric sequences I stumbled upon?
My questions about boundedness came to mind while remembering Rosenthal's $\ell_1$ Theorem. If every subsymmetric basic sequence is bounded, then that theorem would allow you to conclude that a subsequence is either weakly Cauchy or equivalent to the canonical basis of $\ell_1$. But a weakly Cauchy sequence need not be weakly null, right? Anyway, the conclusion would not be the same as the conclusion of the statement that originated my question.
