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Orthogonality in \(C^{*}\)-algebras

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The aim in this paper is to study algebraic orthogonality between positive elements of a \(C^{*}\)-algebra in the context of geometric orthogonality. It has been shown that the algebraic orthogonality in certain classes of \(C^{*}\)-algebras is equivalent to geometric orthogonality when supported with some order-theoretic conditions. Further more, algebraic orthogonality between positive elements in a \(C^{*}\)-algebra is also characterized in terms of positive linear functionals.

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Acknowledgments

The author is indebted to B. V. R. Bhat and V. S. Sunder for many fruitful discussions. The author is also grateful to the referee for his valuable suggestions.

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  1. School of Mathematical Science, National Institute of Science Education and Research, Institute of Physics Campus, Sachivalaya Marg, P. O. Sainik School, Bhubaneswar, 751005, India

    Anil Kumar Karn

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  1. Anil Kumar Karn
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Correspondence to Anil Kumar Karn.

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Karn, A.K. Orthogonality in \(C^{*}\)-algebras. Positivity 20, 607–620 (2016). https://doi.org/10.1007/s11117-015-0375-z

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