Skew-symmetric operators and reflexivity

TL;DR

This paper demonstrates that subspaces of skew-C symmetric operators are reflexive and hyperreflexive, providing bounds on the hyperreflexivity constant, contrasting with the properties of C-symmetric operators.

Contribution

It establishes reflexivity and hyperreflexivity of skew-C symmetric operator subspaces, including bounds on the hyperreflexivity constant, which was previously unknown.

Findings

Skew-C symmetric operator subspaces are reflexive.

These subspaces are hyperreflexive with constant ≤ 3.

Contrasts with properties of C-symmetric operators.

Abstract

In contrast to the subspaces of all $C$-symmetric operators, we show that the subspaces of all skew-C symmetric operators are reflexive and even hyperreflexive with the constant $\kappa(\C^s)\leqslant 3$.