Quasi-inner product spaces of quasi-Sobolev spaces and their completeness

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Jawad Kadhim Khalaf Al-Delfi


      Sequences spaces  , m  ,  p  have called quasi-Sobolev spaces were  introduced   by Jawad . K. Al-Delfi in 2013  [1]. In this  paper , we deal with notion of  quasi-inner product  space  by using concept of  quasi-normed  space which is generalized  to normed space and given a  relationship  between  pre-Hilbert space and a  quasi-inner product space with important  results   and   examples.  Completeness properties in quasi-inner   product space gives  us  concept of  quasi-Hilbert space .  We show  that ,  not  all  quasi-Sobolev spaces  ,  are  quasi-Hilbert spaces. The  best  examples which are  quasi-Hilbert spaces and Hilbert spaces  are , where  m  . Finally, propositions, theorems and examples are our own unless otherwise referred.  


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KHALAF AL-DELFI, Jawad Kadhim. Quasi-inner product spaces of quasi-Sobolev spaces and their completeness. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], p. 337-343, apr. 2018. ISSN 2521-3407. Available at: <https://jih.uobaghdad.edu.iq/index.php/j/article/view/1806>. Date accessed: 28 july 2021. doi: http://dx.doi.org/10.30526/2017.IHSCICONF.1806.