Quasi-compactness in a quasi-Banach space for the sequence space , p 0 p 1 has been introduced based on
the important extension of Milman’s reverse Brunn-Minkowiski inequality by Bastero et al. in 1995. Moreover, Many
interesting results connected with quasi-compactness and quasi-completeness in a quasi-normed space , p for
0 p 1 have been explored. Furthermore, we have shown that, the quasi-normed space under which condition is a
quasi Banach space. Also, we have shown that the space if it is quasi-compact in quasi normed space then it is a quasi-
Banach space and the converse is not true. Finally, a sufficient condition of the existence for a quasi-compact operator
from p p has been presented and analyzed.
رحيم احمد منصور الصفوري | Raheam Ahmad Mansor Al-Saphory | 6375