A type (4) space in (FR)-classification
  We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis. 
Spiros A. Argyros, Antonis Manoussakis, Anna Pelczar-Barwacz
math.FA