Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces

Authors

  • Assadollah Niknam professor
  • Mohammad Janfada associate professor
  • Saeedeh Shamsi Gamchi Ph.D student
Abstract:

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we introduce the notion of algebraically cone metric and we will show that every algebraically cone metric space has a topology.

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Journal title

volume 9  issue None

pages  71- 80

publication date 2014-05

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