Riesz bases in quaternionic Hilbert spaces
S.K. Sharma, Virender, and S.K. Kaushik
TL;DR
This paper introduces and analyzes Riesz bases in quaternionic Hilbert spaces, establishing their properties and relation to frames, and providing foundational results for quaternionic functional analysis.
Contribution
It is the first to systematically study Riesz bases in quaternionic Hilbert spaces, including their characterization and relation to Riesz sequences and frames.
Findings
Riesz bases are frames in quaternionic Hilbert spaces
Equivalence between Riesz bases and complete Riesz sequences
Foundational results on Riesz bases in quaternionic settings
Abstract
In this article, we introduce and study Riesz bases in a separable quaternionic Hilbert spaces. Some results on Riesz bases in a separable quaternionic Hilbert spaces are proved. It is also proved that a Riesz basis in a separable quaternionic Hilbert space a frame for the quaternionic Hilbert space. Riesz sequences are defined and equivalence of a Riesz basis and a complete Riesz sequence in a separable quaternionic Hilbert space is proved.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Algebraic and Geometric Analysis · Advanced Differential Geometry Research