Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w, α, θ) and obtain their (w, α, θ)-Dual spaces. Moreover, we show that the generalized Figà-Talamanca-Herz algebras have an approximation property when G is a proper discrete group and satisfies the p-RD property.
Cheng YAN
. THE APPROXIMATION PROPERTY OF GENERALIZED FIGÀ-TALAMANCA-HERZ ALGEBRAS[J]. Acta mathematica scientia, Series B, 2019
, 39(5)
: 1330
-1338
.
DOI: 10.1007/s10473-019-0511-0
[1] Brodzki J, Niblo G A. Approximation properties for discrete groups//C*-algebras and Elliptic Theory. Basel:Birkhäuser, 2006:23-35
[2] Bo·zejko M. Positive and negative definite kernels on groups. Heidelberg Lectures Notes, 1987
[3] Dales H G, Lau A T-M. The second duals of Beurling algebras. Memoirs of the American Mathematical Society, 2005, 177(836):191
[4] Daws M, Spronk N. On convoluters on Lp-spaces. Studia Mathematica, 2018
[5] Figà-Talamanca A, Picardello M A. Harmonic Analysis on Free Groups. New York:Marcel Dekker Inc, 1983
[6] Forrest B, Kaniuth E, Lau A T, et al. Ideals with bounded approximate identities in Fourier algebras. Journal of Functional Analysis, 2003, 203(1):286-304
[7] Guimei An, Jung-Jin Lee, Zhong-Jin Ruan. On p-approximation properties for p-operator spaces. Journal of Functional Analysis, 2010, 259(4):933-974
[8] Haagerup U. An example of a non-nuclear C*-algebra which has the metric approximation property. Inventiones Mathematicae, 1979, 50(3):279-293
[9] Haagerup U, Kraus J. Approximation properties for group C*-algebras and group von Neumann algebras. Transactions of the American Mathematical Society, 1994, 344(2):667-699
[10] Herz C. The theory of p-spaces with an application to convolution operators. Transactions of the American Mathematical Society, 1971, 154(FEB):69-82
[11] Lee H H, Samei E. Beurling-Fourier algebras, operator amenability and Arens regularity. Journal of Functional Analysis, 2010, 262(1):167-209
[12] Leptin H. Sur lálgèbre de Fourier dún groupe localement compact. C R Acad Sci Paris Sér A-B, 1968:1180-1182
[13] Miao T. Predual of the multiplier algebra of Ap(G) and amenability. Canadian Journal of Mathematics, 2004, 56(2):344-355
[14] Miao T. Approximation properties and approximate identities of Ap(G). Transactions of the American Mathematical Society, 2009, 361(3):1581-1595
[15] Öztop S, Runde V, Spronk N. Beurling-figà-talamanca-herz algebras. Studia Mathematica, 2012, 210(2):117-135
[16] Pisier G, Xu Q. Non-commutative Lp-spaces//Handbook of the Geometry of Banach Spaces, Vol 2. Amsterdam:Elsevier, 2003:1459-1517
[17] Yan C, Bekjan T. Toeplitz operators associated with semifinite von Neumann algebra. Acta Mathematica Scientia, 2015, 35B(1):182-188
[18] Yan C. The Hankel operators and noncommutative BMO spaces. Annals of Functional Analysis, 2016, 7(3):402-410
[19] Xu Q. Non-commutative Lp-spaces. Preprint
[20] Han Y, Bekjan T. The dual of noncommutative Lorentz spaces. Acta Mathematica Scientia, 2011, 31B(5):2067-2080
