Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Isolated points of the spectra of conservative matrices


Author: N. K. Sharma
Journal: Proc. Amer. Math. Soc. 51 (1975), 74-78
MSC: Primary 40C05; Secondary 15A18
DOI: https://doi.org/10.1090/S0002-9939-1975-0372461-3
MathSciNet review: 0372461
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. P. Agnew, On Hurwitz-Silverman-Hausdorff methods of summability, Tôhoku Math. J. 49 (1942), 1-14. MR 7, 433. MR 0015524 (7:433a)
  • [2] G. H. Hardy, Divergent series, Clarendon Press, Oxford, 1949. MR 11, 25. MR 0030620 (11:25a)
  • [3] W. A. Hurwitz and L. L. Silverman, On the consistency and equivalence of certain definitions of summability, Trans. Amer. Math. Soc. 18 (1917), 1-20. MR 1501058
  • [4] Gerald Leibowitz, Discrete Hausdorff transformations, Proc. Amer. Math. Soc. 38 (1973), 541-544. MR 47 #4057. MR 0315508 (47:4057)
  • [5] H. R. Pitt, Mercerian theorems, Proc. Cambridge Philos. Soc. 34 (1938), 510-520.
  • [6] F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Akad. Kiadó, Budapest, 1953; English transl., Ungar, New York, 1955. MR 15, 132; 17, 175. MR 0056821 (15:132d)
  • [7] B. E. Rhoades, Size of convergence domains for known Hausdorff prime matrices, J. Math. Anal. Appl. 19 (1967), 457-468. MR 35 #3316. MR 0212444 (35:3316)
  • [8] .W. W. Rogosinski, On Hausdorff's method of summability, Proc. Cambridge Philos. Soc. 38 (1942), 166-192. MR 3, 296. MR 0006380 (3:296a)
  • [9] N. K. Sharma, Spectra of conservative matrices, Proc. Amer. Math. Soc. 35 (1972), 515-518. MR 46 #5891. MR 0306769 (46:5891)
  • [10] -, Hausdorff operators, Acta Sci. Math. (Szeged) 35 (1973), 165-167. MR 0338824 (49:3588)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 40C05, 15A18

Retrieve articles in all journals with MSC: 40C05, 15A18


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372461-3
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society