Isolated points of the spectra of conservative matrices

Sharma, N. K.

doi:10.1090/S0002-9939-1975-0372461-3

Isolated points of the spectra of conservative matrices
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by N. K. Sharma

Proc. Amer. Math. Soc. 51 (1975), 74-78

DOI: https://doi.org/10.1090/S0002-9939-1975-0372461-3

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Abstract:

We show that the only possible isolated points in the spectrum of a conservative triangular matrix are its diagonal elements, and that any Hausdorff method corresponding to an absolutely continuous mass function is in the norm closure of the analytic methods.

References

Ralph Palmer Agnew, On Hurwitz-Silverman-Hausdorff methods of summability, Tôhoku Math. J. 49 (1942), 1–14. MR 15524
G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
Wallie Abraham Hurwitz and L. L. Silverman, On the consistency and equivalence of certain definitions of summability, Trans. Amer. Math. Soc. 18 (1917), no. 1, 1–20. MR 1501058, DOI 10.1090/S0002-9947-1917-1501058-2
Gerald Leibowitz, Discrete Hausdorff transformations, Proc. Amer. Math. Soc. 38 (1973), 541–544. MR 315508, DOI 10.1090/S0002-9939-1973-0315508-0

Mercerian theorems

34

Frédéric Riesz and Béla Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1953 (French). 2ème éd. MR 0056821
B. E. Rhoades, Size of convergence domains for known Hausdorff prime matrices, J. Math. Anal. Appl. 19 (1967), 457–468. MR 212444, DOI 10.1016/0022-247X(67)90004-2
W. W. Rogosinski, On Hausdorff’s methods of summability, Proc. Cambridge Philos. Soc. 38 (1942), 166–192. MR 6380
N. K. Sharma, Spectra of conservative matrices, Proc. Amer. Math. Soc. 35 (1972), 515–518. MR 306769, DOI 10.1090/S0002-9939-1972-0306769-1
N. K. Sharma, Hausdorff operators, Acta Sci. Math. (Szeged) 35 (1973), 165–167. MR 338824