Agus L. Soenjaya
Department of Mathematics, National University of Singapore,

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ON STRONG AND WEAK CONVERGENCE IN $n-$HILBERT SPACES Soenjaya, Agus L.
Journal of the Indonesian Mathematical Society Volume 19 Number 2 (October 2013)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.19.2.164.79-87

Abstract

We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.DOI : http://dx.doi.org/10.22342/jims.19.2.164.79-87
ON n-BOUNDED AND n-CONTINUOUS OPERATOR IN n-NORMED SPACE Soenjaya, Agus L.
Journal of the Indonesian Mathematical Society Volume 18 Number 1 (April 2012)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.18.1.109.45-56

Abstract

In this paper, the concepts of bounded and continuous n-linear operatorsin n-normed space are discussed. The notions of n-bounded and n-continuous linear operators are then introduced as an extension. This is a generalization of the concepts introduced in [9] and [3]. In addition, the properties of the corresponding spaces of operators are studied to obtain results analogous to the case of normed space. Finally, a sufficient condition for each corresponding space of operators tobe a Banach space is given.DOI : http://dx.doi.org/10.22342/jims.18.1.109.45-56