Continuity of spectrum and spectral radius in algebras of operators

Laura Burlando

Annales de la Faculté des sciences de Toulouse : Mathématiques (1988)

  • Volume: 9, Issue: 1, page 5-54
  • ISSN: 0240-2963

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Burlando, Laura. "Continuity of spectrum and spectral radius in algebras of operators." Annales de la Faculté des sciences de Toulouse : Mathématiques 9.1 (1988): 5-54. <http://eudml.org/doc/73190>.

@article{Burlando1988,
author = {Burlando, Laura},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {spectral continuity in the algebra of linear and continuous operators on a Banach space; continuity of the spectrum and spectral radius functions; continuity points of the spectrum},
language = {eng},
number = {1},
pages = {5-54},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Continuity of spectrum and spectral radius in algebras of operators},
url = {http://eudml.org/doc/73190},
volume = {9},
year = {1988},
}

TY - JOUR
AU - Burlando, Laura
TI - Continuity of spectrum and spectral radius in algebras of operators
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1988
PB - UNIVERSITE PAUL SABATIER
VL - 9
IS - 1
SP - 5
EP - 54
LA - eng
KW - spectral continuity in the algebra of linear and continuous operators on a Banach space; continuity of the spectrum and spectral radius functions; continuity points of the spectrum
UR - http://eudml.org/doc/73190
ER -

References

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  1. [AFHV] Apostol ( C.) Fialkow ( L.A.) Herrero ( D.A.) and Voiculescu ( D.). — Approximation of Hilbert space operators, Volume II. - Research Notes in Mathematics102, Pitman, Boston, 1984. Zbl0572.47001MR735080
  2. [B] Burlando ( L.).—On two subsets of a Banach algebra that are related to the continuity of spectrum and spectral radius, Linear Algebra Appl., t. 84, 1986, p. 251-269. Zbl0612.46046MR872287
  3. [It] Čech ( E.).— Topological Spaces.—John Wiley & Sons, London, 1966. Zbl0141.39401
  4. [CM] Conway ( J.B.) and Morrel ( B.B.).- Operators that are points of spectral continuity, Integral Equations and Operator Theory, t. 2, 1979, p. 174-198. Zbl0419.47001MR543882
  5. [CPY] Caradus ( S.R.) Pfaffenberger ( W.E.) and Yood ( B.).— Calkin Algebras and Algebras of Operators on Banach Spaces. - Lecture Notes in Pure and Applied Mathematics9, Dekker, New York, 1974. Zbl0299.46062MR415345
  6. [DS] Dunford ( N.) and Schwartz ( J.T.).— Linear Operators I.— Interscience, New York, 1958. Zbl0084.10402MR117523
  7. [Ha] Halmos ( P.R.).—A Hilbert Space Problem Book. — Van Nostrand, Princeton, 1967. Zbl0144.38704MR208368
  8. [He] Herrero ( D.A.).— Approximation of Hilbert space operators, volume I.— Research Notes in Mathematics72, Pitman, Boston, 1982. Zbl0494.47001MR676127
  9. [HY] Hocking ( J.G.) and Young ( G.S.).— Topology.—Addison-Wesley, Reading (Massachusetts), 1961. Zbl0135.22701MR125557
  10. [Ka] Kato ( T.).— Perturbation theory for linear operators.—Springer, Berlin, 1966. Zbl0148.12601
  11. [Kö] Köthe ( G.).— Topological vectors spaces I.— Springer, Berlin, 1969. Zbl0179.17001
  12. [M] Murphy ( G.J.).-Continuity of the spectrum and spectral radius, Proc. Amer. Math. Soc., t. 82, 1981, p. 619-621. Zbl0474.46038MR614889
  13. [P] Pietsch ( A.). - Zur Theorie der σ-Transformationen in lokalkonvexen Vektorräu men, Math. Nachr., t. 21, 1960, p. 347-369. Zbl0095.30903MR123185
  14. [R] Rickart ( C.E.).- General Theory of Banach Algebras.- Van Nostrand, Princeton, 1960. Zbl0095.09702MR115101
  15. [TL] Taylor ( A.E.) and Lay ( D.C.).— Introduction to Functional Analysis.—second edition John Wiley & Sons, New York, 1980. Zbl0501.46003

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