In this article we provide the characterization of analysis suitable T-spline spaces (Beirão da Veiga et al., 2013) as the space of piecewise polynomials with appropriate linear constrains on the subdomain interfaces. We describe AST-meshes for which the linear constrains are equivalent to smoothness conditions and provide examples showing that this is not always the case. © 2015 Elsevier B.V. All rights reserved.