Local spectrum and Kaplansky's theorem on algebraic operators

Driss Drissi

Colloquium Mathematicae (1998)

  • Volume: 75, Issue: 2, page 159-165
  • ISSN: 0010-1354

Abstract

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Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.

How to cite

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Drissi, Driss. "Local spectrum and Kaplansky's theorem on algebraic operators." Colloquium Mathematicae 75.2 (1998): 159-165. <http://eudml.org/doc/210534>.

@article{Drissi1998,
abstract = {Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.},
author = {Drissi, Driss},
journal = {Colloquium Mathematicae},
keywords = {local spectral radius; local spectrum; algebraic operators; Kaplansky's theorem},
language = {eng},
number = {2},
pages = {159-165},
title = {Local spectrum and Kaplansky's theorem on algebraic operators},
url = {http://eudml.org/doc/210534},
volume = {75},
year = {1998},
}

TY - JOUR
AU - Drissi, Driss
TI - Local spectrum and Kaplansky's theorem on algebraic operators
JO - Colloquium Mathematicae
PY - 1998
VL - 75
IS - 2
SP - 159
EP - 165
AB - Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.
LA - eng
KW - local spectral radius; local spectrum; algebraic operators; Kaplansky's theorem
UR - http://eudml.org/doc/210534
ER -

References

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  1. [1] B. Aupetit, A Primer on Spectral Theory, Springer, 1991. 
  2. [2] B. Aupetit and D. Drissi, Local spectrum and subharmonicity, Proc. Edinburgh Math. Soc. 39 (1996), 571-579. Zbl0861.47003
  3. [3] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, 1968. 
  4. [4] N. Dunford, A survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217-274. Zbl0088.32102
  5. [5] I. Erdelyi and R. Lange, Spectral Decompositions on Banach Spaces, Lecture Notes in Math. 623, Springer, 1977. Zbl0381.47001
  6. [6] C. Foiaş and F.-H. Vasilescu, On the spectral theory of commutators, J. Math. Anal. Appl. 31 (1970), 473-486. Zbl0175.13604
  7. [7] J. D. Gray, Local analytic extensions of the resolvent, Pacific J. Math. 27 (1968), 305-324. Zbl0172.17204
  8. [8] P. R. Halmos, A Hilbert Space Problem Book, D. Van Nostrand, 1967. 
  9. [9] I. Kaplansky, Infinite Abelian Groups, Univ. of Michigan Press, 1969. 
  10. [10] P. Vrbová, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23 (1973), 483-492. Zbl0268.47006

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