Konca, S., Idris, M., Gunawan, H. (2016). A new 2-inner product on the space of p -summable sequences. test, 24(2), 240-249. doi: 10.1016/j.joems.2015.07.001
Sükran Konca; Mochammad Idris; Hendra Gunawan. "A new 2-inner product on the space of p -summable sequences". test, 24, 2, 2016, 240-249. doi: 10.1016/j.joems.2015.07.001
Konca, S., Idris, M., Gunawan, H. (2016). 'A new 2-inner product on the space of p -summable sequences', test, 24(2), pp. 240-249. doi: 10.1016/j.joems.2015.07.001
Konca, S., Idris, M., Gunawan, H. A new 2-inner product on the space of p -summable sequences. test, 2016; 24(2): 240-249. doi: 10.1016/j.joems.2015.07.001

A new 2-inner product on the space of p -summable sequences

Journal of the Egyptian Mathematical Society
Volume 24, Issue 2, 2016, Pages 240-249    PDF (375.8 K)
DOI: 10.1016/j.joems.2015.07.001
Authors
Sükran Konca1; Mochammad Idris2; Hendra Gunawan2
1Department of Mathematics, Bitlis Eren University, 13000, Bitlis, Turkey
2Department of Mathematics, Institute of Technology Bandung, Bandung 40132, Indonesia
Abstract
In this paper, we wish to define a 2-inner product, non-standard, possibly with weights,
on  p . For this purpose, we aim to obtain a different 2-norm  ., .  2, v , w , which is not equivalent to
the usual 2-norm  ., .  p on  p (except with the condition p = 2 ), satisfying the parallelogram law. We
discuss the properties of the induced 2-norm  ., .  2, v , w and its relationships with the usual 2-norm on
 p . We also find that the 2-inner product  ., .|.  v , w is actually defined on a larger space.
Keywords
2-inner product spaces; 2-normed spaces; p -summable sequences; Weights
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