On Beurling measure algebras

Ross Stokke

Commentationes Mathematicae Universitatis Carolinae (2022)

  • Volume: 62 63, Issue: 2, page 169-187
  • ISSN: 0010-2628

Abstract

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We show how the measure theory of regular compacted-Borel measures defined on the -ring of compacted-Borel subsets of a weighted locally compact group provides a compatible framework for defining the corresponding Beurling measure algebra , thus filling a gap in the literature.

How to cite

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Stokke, Ross. "On Beurling measure algebras." Commentationes Mathematicae Universitatis Carolinae 62 63.2 (2022): 169-187. <http://eudml.org/doc/298503>.

@article{Stokke2022,
abstract = {We show how the measure theory of regular compacted-Borel measures defined on the $\delta $-ring of compacted-Borel subsets of a weighted locally compact group $(G,\omega )$ provides a compatible framework for defining the corresponding Beurling measure algebra $\{\mathcal \{M\}\}(G,\omega )$, thus filling a gap in the literature.},
author = {Stokke, Ross},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted locally compact group; group algebra; measure algebra; Beurling algebra},
language = {eng},
number = {2},
pages = {169-187},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Beurling measure algebras},
url = {http://eudml.org/doc/298503},
volume = {62 63},
year = {2022},
}

TY - JOUR
AU - Stokke, Ross
TI - On Beurling measure algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2022
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62 63
IS - 2
SP - 169
EP - 187
AB - We show how the measure theory of regular compacted-Borel measures defined on the $\delta $-ring of compacted-Borel subsets of a weighted locally compact group $(G,\omega )$ provides a compatible framework for defining the corresponding Beurling measure algebra ${\mathcal {M}}(G,\omega )$, thus filling a gap in the literature.
LA - eng
KW - weighted locally compact group; group algebra; measure algebra; Beurling algebra
UR - http://eudml.org/doc/298503
ER -

References

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  1. Bonsall F. F., Duncan J., Complete Normed Algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, 80, Springer, New York, 1973. Zbl0271.46039MR0423029
  2. Dales H. G., Banach Algebras and Automatic Continuity, London Mathematical Society Monographs, New Series, 24; Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000. MR1816726
  3. Dales H. G., Lau A. T.-M., The second duals of Beurling algebras, Mem. Amer. Math. Soc. 177 (2005), no. 836, vi + 191 pages. MR2155972
  4. Fell J. M. G., Doran R. S., Representations of -algebras, Locally Compact Groups, and Banach -algebraic Bundles, Vol. 1, Basic Representation Theory of Groups and Algebras, Pure and Applied Mathematics, 125, Academic Press, Boston, 1988. MR0936628
  5. Ghahramani F., 10.2140/pjm.1984.113.77, Pacific J. Math. 113 (1984), no. 1, 77–84. MR0745596DOI10.2140/pjm.1984.113.77
  6. Ghahramani F., 10.1090/S0002-9939-1984-0722417-9, Proc. Amer. Math. Soc. 90 (1984), no. 1, 71–76. MR0722417DOI10.1090/S0002-9939-1984-0722417-9
  7. Ghahramani F., Zadeh S., 10.4153/CJM-2016-028-5, Canad. J. Math. 69 (2017), no. 1, 3–20. MR3589852DOI10.4153/CJM-2016-028-5
  8. Grønbæk N., 10.1090/S0002-9947-1990-0962282-5, Trans. Amer. Math. Soc. 319 (1990), no. 2, 765–775. MR0962282DOI10.1090/S0002-9947-1990-0962282-5
  9. Hewitt E., Ross K. A., Abstract Harmonic Analysis, Vol. I: Structure of Topological Groups. Integration Theory, Group Representations, Die Grundlehren der mathematischen Wissenschaften, 115, Academic Press, New York; Springer, Berlin, 1963. MR0156915
  10. Ilie M., Stokke R., 10.1017/S0305004108001199, Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 1, 107–120. MR2431642DOI10.1017/S0305004108001199
  11. Kaniuth E., 10.1007/978-0-387-72476-8, Graduate Texts in Mathematics, 246, Springer, New York, 2009. MR2458901DOI10.1007/978-0-387-72476-8
  12. Kroeker M. E., Stephens A., Stokke R., Yee R., 10.1016/j.jmaa.2021.125935, J. Math. Anal. Appl. 509 (2022), no. 1, Paper No. 125935, 25 pages. MR4355933DOI10.1016/j.jmaa.2021.125935
  13. Lau A. T.-M., 10.4064/cm-39-2-351-359, Colloq. Math. 39 (1978), no. 2, 351–359. MR0522378DOI10.4064/cm-39-2-351-359
  14. Palmer T. W., Banach Algebras and the General Theory of -algebras, Vol. I., Algebras and Banach algebras, Encyclopedia of Mathematics and Its Applications, 49, Cambridge University Press, Cambridge, 1994. MR1270014
  15. Reiter H., Stegeman J. D., Classical Harmonic Analysis and Locally Compact Groups, London Mathematical Society Monographs, New Series, 22, The Clarendon Press, Oxford University Press, New York, 2000. MR1802924
  16. Runde V., 10.7146/math.scand.a-14452, Math. Scand. 95 (2004), no. 1, 124–144. MR2091485DOI10.7146/math.scand.a-14452
  17. Samei E., 10.1016/j.jmaa.2008.05.085, J. Math. Anal. Appl. 346 (2008), no. 2, 451–467. MR2431541DOI10.1016/j.jmaa.2008.05.085
  18. Shepelska V., Zhang Y., 10.1512/iumj.2018.67.6287, Indiana Univ. Math. J. 67 (2018), no. 1, 119–150. MR3776016DOI10.1512/iumj.2018.67.6287
  19. Zadeh S., Isomorphisms of Banach Algebras Associated with Locally Compact Groups, PhD Thesis, University of Manitoba, Canada, 2015. 
  20. Zadeh S., 10.1016/j.jmaa.2016.01.060, J. Math. Anal. Appl. 438 (2016), no. 1, 1–13. MR3462562DOI10.1016/j.jmaa.2016.01.060

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