Some properties of orthonormal sets on inner product quasilinear spaces
Küçük Resim Yok
Tarih
2016
Yazarlar
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Dergi ISSN
Cilt Başlığı
Yayıncı
Matematikçiler Derneği
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Aseev introduced the notion of quasilinear space and normed quasilinear space [1].
Then he gives some basic definition and theorems related to these spaces. We can see in [1]
that, as different from linear spaces, Aseev used the partial order relation when he defined
quasilinear spaces and so he can give consistent counterparts of results in linear spaces. This
pioneering work has motivated us to introduce the concept of inner product quasilinear spaces
and Hilbert
Quasilinear spaces which were given in [5]. Our research with these spaces continued to
investigate the quasilinear counterparts of fundamental theorems in linear functional analysis.
While working in this nonlinear spaces, we have noticed that the new definition is necessary.
So, in this study, we give some new concepts related to inner product quasilinear spaces.
In this paper, we present some properties of orthogonal and orthonormal sets on inner
product quasilinear spaces. We introduce solid floored quasilinear spaces to deal with a better
and suitable kind of quasilinear spaces. To define some topics such as Schauder basis,
complete orthonormal sequence, orthonormal basis and complete set and some related
theorems this classification is crucial. Furthermore, we try to display some geometric
differences of inner product quasilinear spaces from the inner product (linear) spaces.
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Künye
Bozkurt, H., Yılmaz, Y. (2016). Some properties of orthonormal sets on inner product quasilinear spaces. International Conference on Mathematics and Mathematics Education (ICMME-2016), 12-14 May 2016, Elazığ.
