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Para-Banach Space for the Sequence Space ,P 10p | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 19, Issue 1, 2008, Pages 35-42 | ||
| Author | ||
| Kadhim Khalaf Al-Delf | ||
| Abstract | ||
| In [1] , the concept of a quasi - Banach space for the sequence space 0 p 1 was introduced by Jawad . K.Al -Delfi. In this paper , we introduce the notion of a para-Banach space for the sequence space , P 0 p 1 . This concept is based on the important extension of a para-normed space concept as defined in [2]. We consider the sequence space , P 0 p 1 and prove this space is a para-normed space , but it is not a normed space. We study convergence of the sequences in a para-normed space and introduce the concept of a para- Banach space .We also show that every Banach space is a para-Banach space , but the converse is not true. Key words: Sequence space , P 0 p 1 , para-normed space, para-metric space, para-Banach space. | ||
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