Quasi-Compactness in Quasi-Banach Spaces
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2013, Vol 4, Issue 1
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.
Authors and Affiliations
Raheam A. Mansor Al-Saphory, Mahmood K Jasim
Keywords
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- EP ID EP651213
- DOI 10.24297/jam.v4i1.7227
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