


Paper Title:
On Reformations of 2Hilbert Spaces
Author(s):
M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho
Department of Mathematics, Semnan
University,
P.O. Box 35195363, Semnan,
Iran
meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com
Department of Mathematics, Semnan
University,
Iran
Department of Mathematics, Semnan
University,
Iran
safi@semnan.ac.ir, SafiMohammadReza@yahoo.com
Department of Mathematics Education and
the RINS,
Gyeongsang National University
Chinju 660701,
Korea
Abstract:
In this paper, first, we introduce the new concept of (complex) 2Hilbert spaces, that is, we define the concept of 2inner product spaces with a complex valued 2inner product by using the 2norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2Hilbert spaces.
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