Generalized spectral perturbation and the boundary spectrum

Sonja Mouton

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 603-621
  • ISSN: 0011-4642

Abstract

top
By considering arbitrary mappings ω from a Banach algebra A into the set of all nonempty, compact subsets of the complex plane such that for all a ∈ A , the set ω ( a ) lies between the boundary and connected hull of the exponential spectrum of a , we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.

How to cite

top

Mouton, Sonja. "Generalized spectral perturbation and the boundary spectrum." Czechoslovak Mathematical Journal 71.2 (2021): 603-621. <http://eudml.org/doc/298257>.

@article{Mouton2021,
abstract = {By considering arbitrary mappings $\omega $ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$, the set $\omega (a)$ lies between the boundary and connected hull of the exponential spectrum of $a$, we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.},
author = {Mouton, Sonja},
journal = {Czechoslovak Mathematical Journal},
keywords = {exponential spectrum; singular spectrum; boundary spectrum; boundary and hull; (strong) Riesz property; Mobius spectrum},
language = {eng},
number = {2},
pages = {603-621},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized spectral perturbation and the boundary spectrum},
url = {http://eudml.org/doc/298257},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Mouton, Sonja
TI - Generalized spectral perturbation and the boundary spectrum
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 603
EP - 621
AB - By considering arbitrary mappings $\omega $ from a Banach algebra $A$ into the set of all nonempty, compact subsets of the complex plane such that for all $a \in A$, the set $\omega (a)$ lies between the boundary and connected hull of the exponential spectrum of $a$, we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
LA - eng
KW - exponential spectrum; singular spectrum; boundary spectrum; boundary and hull; (strong) Riesz property; Mobius spectrum
UR - http://eudml.org/doc/298257
ER -

References

top
  1. Aupetit, B., 10.1007/BFb0064204, Lecture Notes in Mathematics 735. Springer, Berlin (1979), French. (1979) Zbl0409.46054MR0549769DOI10.1007/BFb0064204
  2. Aupetit, B., 10.1007/978-1-4612-3048-9, Universitext. Springer, New York (1991). (1991) Zbl0715.46023MR1083349DOI10.1007/978-1-4612-3048-9
  3. Burlando, L., 10.1155/S0161171293001036, Int. J. Math. Sci. 16 (1993), 819-822. (1993) Zbl0808.46065MR1234831DOI10.1155/S0161171293001036
  4. Conway, J. B., 10.1007/978-1-4757-4383-8, Graduate Texts in Mathematics 96. Springer, New York (2010). (2010) Zbl0706.46003MR1070713DOI10.1007/978-1-4757-4383-8
  5. Groenewald, L., Harte, R. E., Raubenheimer, H., 10.1080/16073606.1989.9632195, Quaest. Math. 12 (1989), 439-446. (1989) Zbl0705.46022MR1021942DOI10.1080/16073606.1989.9632195
  6. Groenewald, L., Raubenheimer, H., 10.1080/16073606.1988.9632154, Quaest. Math. 11 (1988), 399-408. (1988) Zbl0673.46022MR0969558DOI10.1080/16073606.1988.9632154
  7. Harte, R. E., 10.1090/S0002-9939-1976-0407603-5, Proc. Am. Math. Soc. 58 (1976), 114-118. (1976) Zbl0338.46043MR0407603DOI10.1090/S0002-9939-1976-0407603-5
  8. Harte, R. E., Invertibility and Singularity for Bounded Linear Operators, Pure and Applied Mathematics 109. Marcel Dekker, New York (1988). (1988) Zbl0636.47001MR0920812
  9. Harte, R. E., Wickstead, A. W., Boundaries, hulls and spectral mapping theorems, Proc. R. Ir. Acad., Sect. A 81 (1981), 201-208. (1981) Zbl0489.46041MR0654819
  10. Lindeboom, L., Raubenheimer, H., A note on the singular spectrum, Extr. Math. 13 (1998), 349-357. (1998) Zbl1054.46510MR1695568
  11. Lindeboom, L., Raubenheimer, H., 10.1216/rmjm/1181071617, Rocky Mt. J. Math. 29 (1999), 957-970. (1999) Zbl0969.46038MR1733077DOI10.1216/rmjm/1181071617
  12. Lindeboom, L., Raubenheimer, H., 10.1023/A:1021727829750, Czech. Math. J. 52 (2002), 565-574. (2002) Zbl1010.46045MR1923262DOI10.1023/A:1021727829750
  13. Mouton, H. du T., 10.1080/16073606.1994.9632217, Quaest. Math. 17 (1994), 59-66. (1994) Zbl0818.46053MR1276008DOI10.1080/16073606.1994.9632217
  14. Mouton, H. du T., Mouton, S., Raubenheimer, H., 10.2989/16073606.2011.622893, Quaest. Math. 34 (2011), 341-359. (2011) Zbl1274.46095MR2844530DOI10.2989/16073606.2011.622893
  15. Mouton, H. du T., Raubenheimer, H., 10.1080/16073606.1991.9631656, Quaest. Math. 14 (1991), 371-382. (1991) Zbl0763.46035MR1143042DOI10.1080/16073606.1991.9631656
  16. Mouton, S., 10.1017/S0004972700035681, Bull. Aust. Math. Soc. 74 (2006), 239-246. (2006) Zbl1113.46044MR2260492DOI10.1017/S0004972700035681
  17. Mouton, S., 10.1215/ijm/1286212914, Ill. J. Math. 53 (2009), 757-767. (2009) Zbl1210.46033MR2727353DOI10.1215/ijm/1286212914
  18. Müller, V., 10.1007/978-3-0348-7788-6, Operator Theory: Advances and Applications 139. Birkhäuser, Basel (2007). (2007) Zbl1208.47001MR2355630DOI10.1007/978-3-0348-7788-6
  19. Raubenheimer, H., Swartz, A., 10.2989/16073606.2018.1501439, Quaest. Math. 42 (2019), 811-822. (2019) Zbl1439.46039MR3989360DOI10.2989/16073606.2018.1501439
  20. Raubenheimer, H., Swartz, A., 10.1216/RMJ-2019-49-8-2747, Rocky Mt. J. Math. 49 (2019), 2747-2754. (2019) Zbl07163196MR4058347DOI10.1216/RMJ-2019-49-8-2747
  21. Taylor, A. E., Lay, D. C., Introduction to Functional Analysis, John Wiley & Sons, New York (1980). (1980) Zbl0501.46003MR0564653
  22. Živkovič-Zlatanovič, S. Č., Harte, R. E., 10.2989/16073606.2015.1026558, Quaest. Math. 38 (2015), 573-586. (2015) Zbl06696038MR3403668DOI10.2989/16073606.2015.1026558

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.