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On the Weak Topology of Quaternionic Hilbert Spaces

  • M. FashandiEmail author
Article
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Abstract

In this paper, we study weak topology on right quaternionic Hilbert spaces. We show that on right quaternionic Hilbert spaces weak compactness and weak sequential compactness coincide which could be viewed as a generalization of Eberlein–Šmulian theorem. Also, we apply this observation on study compact operators on right quaternionic Hilbert spaces.

Keywords

Quaternionic Hilbert spaces Weak topology Compact operators 

Mathematics Subject Classification

46E22 47B07 

Notes

Acknowledgments

The author highly appreciates the reviewers’ insightful and valuable comments. Also, the author thanks Professor Jan Lang from the Ohio State University, for his helpful suggestions on the initial version of this manuscript. This research was supported by a Grant from Ferdowsi University of Mashhad: No. 2/47516.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

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