## Annals of Functional Analysis

### The mathematical work of Anthony To-Ming Lau

#### Abstract

In this paper, we review aspects of the biography and mathematical work of Professor Anthony To-Ming Lau.

#### Article information

Source
Ann. Funct. Anal. Volume 7, Number 1 (2016), 206-216.

Dates
Accepted: 25 November 2015
First available in Project Euclid: 11 January 2016

https://projecteuclid.org/euclid.afa/1452520452

Digital Object Identifier
doi:10.1215/20088752-3462222

Mathematical Reviews number (MathSciNet)
MR3449351

Zentralblatt MATH identifier
1332.01053

Keywords
bibliometrics

#### Citation

Moslehian, M. S.; Neufang, M. The mathematical work of Anthony To-Ming Lau. Ann. Funct. Anal. 7 (2016), no. 1, 206--216. doi:10.1215/20088752-3462222. https://projecteuclid.org/euclid.afa/1452520452

#### References

• [1] W. Bade, H. G. Dales, and Z. A. Lykova, Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 137 (1999), no. 656.
• [2] J. Baker, A. T.-M. Lau, and J. Pym, Module homomorphisms and topological centres associated with weakly sequentially complete Banach algebras, J. Funct. Anal. 158 (1998), no. 1, 186–208.
• [3] G. Choquet and J. Deny, Sur l’équation de convolution $\mu=\mu*\sigma$, C. R. Acad. Sci. Paris 250 (1960), 799–801.
• [4] C.-H. Chu and A. T.-M. Lau, Harmonic Functions on Groups and Fourier Algebras, Lecture Notes in Math. 1782, Springer, Berlin, 2002.
• [5] I. C. Craw and N. J. Young, Regularity of multiplication in weighted group and semigroup algebras, Quart. J. Math. Oxford Ser. (2) 25 (1974), 351–358.
• [6] H. G. Dales, A. T.-M. Lau, and D. Strauss, Banach algebras on semigroups and on their compactifications, Mem. Amer. Math. Soc. 205 (2010), no. 966.
• [7] H. G. Dales and A. T.-M. Lau, The second duals of Beurling algebras, Mem. Amer. Math. Soc. 177 (2005), no. 836.
• [8] G. Fendler, A. T.-M. Lau, and M. 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.
• [9] B. Forrest, Amenability and ideals in $A(G)$, J. Austral. Math. Soc. Ser. A 53 (1992), no. 2, 143–155.
• [10] B. Forrest, E. Kaniuth, A. T.-M. Lau, and N. Spronk, Ideals with bounded approximate identities in Fourier algebras, J. Funct. Anal. 203 (2003), no. 1, 286–304.
• [11] F. Ghahramani and R. J. Loy, Multipliers and ideals in second conjugate algebras related to locally compact groups, J. Funct. Anal. 132 (1995), no. 1, 170–191.
• [12] F. Ghahramani, R. J. Loy, and G. A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Amer. Math. Soc. 124 (1996), no. 5, 1489–1497.
• [13] J. E. Gilbert, On projections of $L^{\infty}(G)$ onto translation-invariant subspaces, Proc. London Math. Soc. (3) 19 (1969), 69–88.
• [14] E. Granirer and A. T.-M. Lau, Invariant means on locally compact groups, Illinois J. Math. 15 (1971), 249–257.
• [15] A. Ya. Helemskii, The Homology of Banach and Topological Algebras, Math. Appl. (Soviet Ser.) 41, Kluwer, Dordrecht, 1989.
• [16] N. Işik, J. Pym, and A. Ülger, The second dual of the group algebra of a compact group, J. London Math. Soc. (2) 35 (1987), no. 1, 135–148.
• [17] E. Kaniuth and A. T.-M. Lau, Extension and separation properties of positive definite functions on locally compact groups, Trans. Amer. Math. Soc. 359 (2007), no. 1, 447–463.
• [18] E. Kaniuth, A. T.-M. Lau, and A. Ülger, Multipliers of commutative Banach algebras, power boundedness and Fourier–Stieltjes algebras, J. Lond. Math. Soc. (2) 81 (2010), no. 1, 255–275.
• [19] E. Kaniuth, A. T.-M. Lau, and A. Ülger, Power boundedness in Fourier and Fourier–Stieltjes algebras and other commutative Banach algebras J. Funct. Anal. 260 (2011), no. 8, 2366–2386.
• [20] E. Kaniuth, A. T.-M. Lau, and A. Ülger, Power boundedness in Banach algebras associated with locally compact groups, Studia Math. 222 (2014), no. 2, 165–189.
• [21] A. T.-M. Lau, Topological semigroups with invariant means in the convex hull of multiplicative means, Trans. Amer. Math. Soc. 148 (1970), 69–84.
• [22] A. T.-M. Lau, Characterizations of amenable Banach algebras, Proc. Amer. Math. Soc. 70 (1978), no. 2, 156–160.
• [23] A. T.-M. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math. 118 (1983), no. 3, 161–175.
• [24] A. T.-M. Lau, Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 2, 273–283.
• [25] A. T.-M. Lau and V. Losert, On the second conjugate algebra of $L_{1}(G)$ of a locally compact group, J. London Math. Soc. (2) 37 (1988), no. 3, 464–470.
• [26] A. T.-M. Lau and J. Ludwig, Fourier–Stieltjes algebra of a topological group, Adv. Math. 229 (2012), no. 3, 2000–2023.
• [27] A. T.-M. Lau and P. F. Mah, Normal structure in dual Banach spaces associated with a locally compact group, Trans. Amer. Math. Soc. 310 (1988), no. 1, 341–353.
• [28] A. T.-M. Lau, N. Shioji, and W. Takahashi, Existence of nonexpansive refractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in Banach spaces, J. Funct. Anal. 161 (1998), 62–75.
• [29] A. T.-M. Lau and W. Takahashi, Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces, Nonlinear Anal. 70 (2009), no. 11, 3837–3841.
• [30] A. T.-M. Lau and W. Takahashi, Weak convergence and nonlinear ergodic theorems for reversible semigroups of nonexpansive mappings, Pacific J. Math. 126 (1987), no. 2, 277–294.
• [31] A. T.-M. Lau and A. Ülgar, Some geometric properties on the Fourier and Fourier–Stieltjes algebras of locally compact groups, Arens regularity and related problems, Trans. Amer. Math. Soc. 337 (1993), no. 1, 321–359.
• [32] A. T.-M. Lau and Y. Zhang, Fixed point properties of semigroups of non-expansive mappings, J. Funct. Anal. 254 (2008), 2513–2533.
• [33] A. T.-M. Lau and Y. Zhang, Finite-dimensional invariant subspace property and amenability for a class of Banach algebras, Trans. Amer. Math. Soc., published electronically 1 July 2015.
• [34] T. C. Lim, Asymptotic centres and nonexpansive mappings in conjugate Banach spaces, Pacific J. Math. 90 (1980), 135–143.
• [35] V. Losert, M. Neufang, J. Pachl, and J. Steprans, Proof of the Ghahramani–Lau conjecture, to appear in Adv. Math., preprint arXiv:1510.05412 [math.FA].
• [36] M. S. Monfared, On certain products of Banach algebras with applications to harmonic analysis, Studia Math. 178 (2007), no. 3, 277–294.
• [37] M. Nemati and H. Javanshiri, Some homological and cohomological notions on $T$-Lau product of Banach algebras, Banach J. Math. Anal. 9 (2015), no. 2, 183–195.
• [38] M. Neufang, On a conjecture by Ghahramani–Lau and related problems concerning topological centres, J. Funct. Anal. 224 (2005), no. 1, 217–229.
• [39] J.-P. Pier, Amenable Locally Compact Groups, Pure Appl. Math. (N.Y.). Wiley, New York, 1984.
• [40] B. M. Schreiber, Measures with bounded convolution powers, Trans. Amer. Math. Soc. 151 (1970), 405–431.