Isometries of combinatorial Tsirelson spaces
Natalia Ma\'slany

TL;DR
This paper characterizes the structure of isometries on a class of Tsirelson-type spaces, showing how they are determined by permutations and sign-changes, with more rigidity in higher-order Schreier families.
Contribution
It extends the characterization of isometries from classical Tsirelson spaces to a broader class involving Schreier families of arbitrary countable order.
Findings
Isometries on $T[ heta, ext{S}_1]$ are determined by permutations and sign-changes.
Isometries on $T[ heta, ext{S}_eta]$ for $eta eq 1$ are solely sign-change operations.
The results generalize previous characterizations to a wider class of Tsirelson-type spaces.
Abstract
We extend existing results that characterize isometries on the Tsirelson-type spaces () to the class (, ), where denote the Schreier families of order . We prove that every isometry on () is determined by a permutation of the first elements of the canonical unit basis followed by a possible sign-change of the corresponding coordinates together with a sign-change of the remaining coordinates. Moreover, we show that for the spaces (, ) the isometries exhibit a more rigid character, namely, they are…
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Holomorphic and Operator Theory
