Spectral characterizations of central elements in Banach algebras

Matej Brešar; Peter Šemrl

Studia Mathematica (1996)

  • Volume: 120, Issue: 1, page 47-52
  • ISSN: 0039-3223

Abstract

top
Let A be a complex unital Banach algebra. We characterize elements belonging to Γ(A), the set of elements central modulo the radical. Our result extends and unifies several known characterizations of elements in Γ(A).

How to cite

top

Brešar, Matej, and Šemrl, Peter. "Spectral characterizations of central elements in Banach algebras." Studia Mathematica 120.1 (1996): 47-52. <http://eudml.org/doc/216319>.

@article{Brešar1996,
abstract = {Let A be a complex unital Banach algebra. We characterize elements belonging to Γ(A), the set of elements central modulo the radical. Our result extends and unifies several known characterizations of elements in Γ(A).},
author = {Brešar, Matej, Šemrl, Peter},
journal = {Studia Mathematica},
keywords = {elements central modulo the radical},
language = {eng},
number = {1},
pages = {47-52},
title = {Spectral characterizations of central elements in Banach algebras},
url = {http://eudml.org/doc/216319},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Brešar, Matej
AU - Šemrl, Peter
TI - Spectral characterizations of central elements in Banach algebras
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 1
SP - 47
EP - 52
AB - Let A be a complex unital Banach algebra. We characterize elements belonging to Γ(A), the set of elements central modulo the radical. Our result extends and unifies several known characterizations of elements in Γ(A).
LA - eng
KW - elements central modulo the radical
UR - http://eudml.org/doc/216319
ER -

References

top
  1. [1] B. Aupetit, A Primer on Spectral Theory, Springer, New York, 1991. 
  2. [2] M. Brešar, Derivations decreasing the spectral radius, Arch. Math. (Basel) 61 (1993), 160-162. Zbl0818.46049
  3. [3] R. E. Curto and M. Mathieu, Spectrally bounded generalized inner derivations, Proc. Amer. Math. Soc. 123 (1995), 2431-2434. Zbl0822.47034
  4. [4] S. Grabiner, The spectral diameter in Banach algebras, ibid. 91 (1984), 59-63. Zbl0562.46028
  5. [5] M. Mathieu, Where to find the image of a derivation, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 1994, 237-249. 
  6. [6] V. Pták, Derivations, commutators and the radical, Manuscripta Math. 23 (1978), 355-362. Zbl0376.46031
  7. [7] V. Pták, Commutators in Banach algebras, Proc. Edinburgh Math. Soc. 22 (1979), 207-211. Zbl0407.46043
  8. [8] J. Zemánek, Idempotents in Banach algebras, Bull. London Math. Soc. 11 (1979), 177-183. Zbl0429.46029
  9. [9] J. Zemánek, Properties of the spectral radius in Banach algebras, in: Spectral Theory, Banach Center Publ. 8, PWN-Polish Scientific Publ., Warszawa, 1982, 579-595. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.