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
  • Views 181
  • Downloads 0

How To Cite

Raheam A. Mansor Al-Saphory, Mahmood K Jasim (2013). Quasi-Compactness in Quasi-Banach Spaces. JOURNAL OF ADVANCES IN MATHEMATICS, 4(1), 325-341. https://europub.co.uk/articles/-A-651213