, Volume 20, Issue 3, pp 607–620 | Cite as

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



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.


Algebraic orthogonality Absolute p-orthogonality Absolute order smooth p-normed spaces Absolute p-orthogonal decomposition 

Mathematics Subject Classification

Primary 46B40 Secondary 46L05 46L30 



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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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematical ScienceNational Institute of Science Education and Research, Institute of Physics CampusBhubaneswarIndia

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