Quasi-Compactness in Quasi-Banach Spaces

Abstract

Quasi-compactness in a quasi-Banach space for the sequence space Lp, 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, Lp 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  quasi Banach  space and the converse is not true. Finally, a sufficient condition of the existence for a quasi-compact operator from Lp -> Lp has been presented and analyzed.