Closed ideals with bounded approximate identities in some Banach algebras
HTML articles powered by AMS MathViewer
- by Issa Mohamadi PDF
- Proc. Amer. Math. Soc. 148 (2020), 3473-3478 Request permission
Abstract:
In this paper, we characterize closed ideals with bounded approximate identities in some Banach algebras. Our results provide answers to a question of Lau and Ülger.References
- H. G. Dales, Banach algebras and automatic continuity, London Mathematical Society Monographs. New Series, vol. 24, The Clarendon Press, Oxford University Press, New York, 2000. Oxford Science Publications. MR 1816726
- Gero Fendler, Anthony To-Ming Lau, and Michael Leinert, Weak${}^\ast$ fixed point property and asymptotic centre for the Fourier-Stieltjes algebra of a locally compact group, J. Funct. Anal. 264 (2013), no. 1, 288–302. MR 2995708, DOI 10.1016/j.jfa.2012.10.011
- Brian Forrest, Amenability and bounded approximate identities in ideals of $A(G)$, Illinois J. Math. 34 (1990), no. 1, 1–25. MR 1031879
- Brian Forrest, Projective operator spaces, almost periodicity and completely complemented ideals in the Fourier algebra, Rocky Mountain J. Math. 41 (2011), no. 1, 155–176. MR 2845938, DOI 10.1216/RMJ-2011-41-1-155
- Anthony To Ming Lau, Invariantly complemented subspaces of $L_{\infty }(G)$ and amenable locally compact groups, Illinois J. Math. 26 (1982), no. 2, 226–235. MR 650390
- Anthony To Ming Lau and Viktor Losert, Weak$^\ast$-closed complemented invariant subspaces of $L_\infty (G)$ and amenable locally compact groups, Pacific J. Math. 123 (1986), no. 1, 149–159. MR 834144
- Anthony To-Ming Lau and Ali Ülger, Characterization of closed ideals with bounded approximate identities in commutative Banach algebras, complemented subspaces of the group von Neumann algebras and applications, Trans. Amer. Math. Soc. 366 (2014), no. 8, 4151–4171. MR 3206455, DOI 10.1090/S0002-9947-2014-06336-8
- Teng-Sun Liu, Arnoud van Rooij, and Ju Kwei Wang, Projections and approximate identities for ideals in group algebras, Trans. Amer. Math. Soc. 175 (1973), 469–482. MR 318781, DOI 10.1090/S0002-9947-1973-0318781-2
- Issa Mohamadi and Shahram Saeidi, Existence and structure of the common fixed points based on TVS, Filomat 31 (2017), no. 6, 1773–1779. MR 3635214, DOI 10.2298/FIL1706773M
- Walter Rudin, Projections on invariant subspaces, Proc. Amer. Math. Soc. 13 (1962), 429–432. MR 138012, DOI 10.1090/S0002-9939-1962-0138012-4
- Peter J. Wood, Complemented ideals in the Fourier algebra of a locally compact group, Proc. Amer. Math. Soc. 128 (2000), no. 2, 445–451. MR 1616589, DOI 10.1090/S0002-9939-99-04989-8
Additional Information
- Issa Mohamadi
- Affiliation: Department of Mathematics, Sanandaj Branch Islamic Azad University, Sanandaj, Iran
- Email: imohamadi@iausdj.ac.ir, imohamadi.maths@gmail.com
- Received by editor(s): October 10, 2019
- Received by editor(s) in revised form: January 10, 2020
- Published electronically: May 8, 2020
- Communicated by: Stephen Dilworth
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3473-3478
- MSC (2010): Primary 46E25, 13B22, 46B80, 46E15, 46J05, 47H09, 37C25, 47L45
- DOI: https://doi.org/10.1090/proc/15021
- MathSciNet review: 4108853