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Spectral, and Numerical Range, Approximants

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Abstract

The theory of spectral approximants presents a precise geometric way of specifying approximants. The theory was initiated by Halmos [22] and later extended to the context of \(\mathcal{C}_{p}\) by Bouldin [11] and Bhatia [8]. More recently the related concept of numerical range approximant was introduced [25].

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Bibliography

  1. S.K. Berberian, The Weyl spectrum of an operator. Indiana Univ. Math. J. 20, 529–544 (1970)

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  2. R. Bhatia, Some inequalities for norm ideals. Commun. Math. Phys. 111, 33–39 (1987)

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  3. R. Bouldin, Best approximation of a normal operator in the Schatten p-norm. Proc. Am. Math. Soc. 80, 277–282 (1980)

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  4. P.R. Halmos, Spectral approximants of normal operators. Proc. Edin. Math. Soc. 19, 51–58 (1974)

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  5. P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)

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  6. R. Khalil, P.J. Maher, Spectral approximation in L(H). Numer. Funct. Anal. Optim. 21(5/6), 693–713 (2000)

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  7. P.J. Maher, Spectral approximants concerning balanced and convex sets. Ann. Univ. Sci. Budapest. 46, 177–181 (2003)

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  8. D.D. Rogers, Approximation by unitary and essentially unitary operators. Acta Sci. Math. 39, 141–151 (1977)

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  9. B. Simon, Trace Ideals and Their Applications (Cambridge University Press, Cambridge, 1979)

    MATH  Google Scholar 

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Maher, P.J. (2017). Spectral, and Numerical Range, Approximants. In: Operator Approximant Problems Arising from Quantum Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61170-9_5

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