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The Rayleigh\(-\)Ritz minimax formula in Kaplansky\(-\)Hilbert modules

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Abstract

We give the Rayleigh\(-\)Ritz minimax formula for cyclically compact operators on Kaplansky\(-\)Hilbert modules.

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References

  1. Allakhverdiev, D.É.: On the rate of approximation of completely continuous operators by finite dimensional operators [in Russian]. Azerb. Gos. Univ. Uchen. Zap. (Baku) 2, 27–37 (1957)

    Google Scholar 

  2. Berberian, S.K.: Baer \(\ast \)-Rings. Springer, Berlin (1972)

    Google Scholar 

  3. Fiedler, M., Pták, V.: Sur la meilleure approximation des transformations lineaires par des transformations de rang prescrit. C.R. Acad. Sci. Paris 254, 3805–3807 (1962)

    MATH  MathSciNet  Google Scholar 

  4. Garling, D.J.H.: Inequalities A Journey into Linear Analysis. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  5. Kaplansky, I.: Modules over operator algebras. Am. J. Math. 75(4), 839–858 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  6. Kusraev, A.G.: Boolean valued analysis of duality between universally complete modules. Dokl. Akad. Nauk SSSR 267(5), 1049–1052 (1982)

    MathSciNet  Google Scholar 

  7. Kusraev, A.G.: Vector Duality and Its Applications [in Russian]. Nauka, Novosibirsk (1985)

    Google Scholar 

  8. Kusraev, A.G.: Cyclically compact operators in Banach spaces. Vladikavkaz Math. J. 2(1), 10–23 (2000)

  9. Kusraev, A.G.: Dominated Operators. Kluwer Academic Publishers, Boston (2000)

    Book  MATH  Google Scholar 

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Acknowledgments

The author sincerely thanks Prof. Anatoly Kusraev for his hospitality during the author’s stay in the Southern Mathematical Institute in Vladikavkaz, Russia, where the present work has been carried out as part of the author’s PhD thesis.

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  1. Department of Mathematics and Computer Science, İstanbul Kültür University, Bakırköy , 34156,  İstanbul, Turkey

    Uğur Gönüllü

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  1. Uğur Gönüllü
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Correspondence to Uğur Gönüllü.

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Gönüllü, U. The Rayleigh\(-\)Ritz minimax formula in Kaplansky\(-\)Hilbert modules. Positivity 19, 347–354 (2015). https://doi.org/10.1007/s11117-014-0301-9

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  • DOI: https://doi.org/10.1007/s11117-014-0301-9

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