For the unit vector basis of has the property of perfect homogeneity: it is equivalent to all its normalized block basic sequences, that is, perfectly homogeneous bases are a special case of symmetric bases. For Banach spaces, a classical result of Zippin (1966) proved that perfectly homogeneous bases are equivalent to either the canonical -basis or the canonical -basis for some . In this note, we show that (a relaxed form of) perfect homogeneity characterizes the unit vector bases of for as well amongst bases in nonlocally convex quasi-Banach spaces.
"On Perfectly Homogeneous Bases in Quasi-Banach Spaces." Abstr. Appl. Anal. 2009 1 - 7, 2009. https://doi.org/10.1155/2009/865371