Pseudo-contractibility Of Weighted Lp -Algebras

Fatemeh Abtahi

doi:10.2478/auom-2013-0038

.blurhash-client-img { display: none !important; }

Pseudo-contractibility Of Weighted Lp -Algebras

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 21 (2013): Issue 3 (November 2013)

By: Fatemeh Abtahi

Open Access

|Mar 2014

Abstract

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L^p-algebra L^1p_ω(G). Here, we establish necessary and sufficient conditions for L^1p_ω(G) to be φ-contractible, pseudo-contractible or contractible. Moreover we give some similar results about L^P(G, ω).

References

[1] F. Abtahi, Lebesgue weighted L^p - algebra on locally compact groups, Acta. Math. Hun- gar., 133/4, (2011), 324-331.10.1007/s10474-011-0097-z
Search in Google Scholar
[2] M. Alaghmandan, R. Nasr Isfahani and M. Nemati, On ф-contractibility of the Lebesgue-Fourier algebra of a locally compact group, Arch. Math. (Basel), 95, (2010), 373-379.10.1007/s00013-010-0177-2
Search in Google Scholar
[3] A. M. Bruckner, Differentiation of integrals, Amer. Math. Monthly, 78 No. 9 pt. 2, (1971).10.2307/3072337
Search in Google Scholar
[4] A. Deitmar and S. Echterhoff, Principles of harmonic analysis, Springer, New York, 2009.
Search in Google Scholar
[5] J. Diestel and J. J. Uhl, Jr., Vector measures, AMS, 1977.10.1090/surv/015
Search in Google Scholar
[6] D. H. Dunford, Segal algebras and left normed ideals, J. London Math. Soc. (2), 8, (1974), 514-516.10.1112/jlms/s2-8.3.514
Search in Google Scholar
[7] R. E. Edwards, The stability of weighted Lebesgue spaces, Trans. Amer. Math. Soc., 93, (1959), 369-394.10.1090/S0002-9947-1959-0112050-4
Search in Google Scholar
[8] H. G. Feichtinger, On a class of convolution algebras of functions, Ann. Inst. Fourier (Grenoble), 27, no. 3, (1977), 135-162.10.5802/aif.665
Search in Google Scholar
[9] H. G. Feichtinger, Some remarks on Banach convolution algebras of functions (*), Istituto Nazionale di Alta Matematica Symposia Mathematica, Volume XXII, (1977), 453-455.
Search in Google Scholar
[10] H. G. Feichtinger, Gewichtsfunktionen auf, lokalkompakten Gruppen, Osterreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II, 188/8-10, (1979), 451-471.
Search in Google Scholar
[11] H. G. Feichtinger, Weighted L^p - spaces and the canonical mapping TH : L¹(G) ^ L¹(G/H), Bollettino U. M. I. (5)16-B, (1979), 989-999.
Search in Google Scholar
[12] H. G. Feichtinger and A. T. Gurkanli, On a family of weighted convolution algebras, Internat. J. Math. Math. Sci., 13/3, (1990), 517-525.10.1155/S0161171290000758
Search in Google Scholar
[13] G. Fendler, K. Grchenig, M. Leinert, J. Ludwig and C. Molitor-Braun, Weighted group algebras on groups of polynomial growth, Math. Z., 245/4, (2003), 791-821.10.1007/s00209-003-0571-6
Search in Google Scholar
[14] F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Cambridge Philos. Soc., 142, (2007), no. 1, 111-123.
Search in Google Scholar
[15] A. Ya. Helemskii, A. Ya. Helemskii, Banach and Locally Convex Algebras, The Clarendon Press Oxford University Press, New York, 1993.
Search in Google Scholar
[16] E. Hewitt and K. Ross, Abstract harmonic analysis I,II, Springer-Verlag, New York, 1970.10.1007/978-3-662-26755-4
Search in Google Scholar
[17] Z. Hu, M. S. Monfared and T. Traynor, On character amenable Banach algebras, Studia Math., 193, (2009), no. 1, 53-78.
Search in Google Scholar
[18] Yu. N. Kuznetsova, Weighted Lp-Algebras on Groups, Funct. Anal. Appl., 40/3, (2006), 234-236.10.1007/s10688-006-0037-9
Search in Google Scholar
[19] Yu. N. Kuznetsova, Invariant weighted algebras L^p(G,w), Mat. Zametki., 84/4, (2008), 567-576.10.4213/mzm3866
Search in Google Scholar
[20] H. Reiter, L¹-algebras and segal algebras, Lecture Notes in Mathematics, 231, Springer-Verlag, Berlin, 1971.10.1007/BFb0060759
Search in Google Scholar
[21] V. Runde, Lectures on amenability, Lecture Notes in Mathematics, 1774, Springer- Verlag, Berlin, 2002.10.1007/b82937
Search in Google Scholar
[22] E. Samei, N. Spronk and R. Stokke, Biflatness and pseudo-amenability of Segal algebras, Canad. J. Math., 62, (2010), no. 4, 845-869.
Search in Google Scholar
[23] Ju. V. Selivanov, Banach Algebras of Small Global Dimension Zero, Uspehi Mat. Nauk., 31, (1976), 227-228.
Search in Google Scholar
[24] J. L. Taylor, Homology and cohomology for topological algebras, Advances in Math., 9, (1972), 137-182.10.1016/0001-8708(72)90016-3
Search in Google Scholar
[25] J. Wermer, On a class of normed rings, Ark. Mat., 2, (1954), 537-551.10.1007/BF02591228
Search in Google Scholar
[26] Y. Zhang, Maximal ideals and the structure of contractible and amenable Banach algebras, Bull. Austral. Math. Soc., 62, (2000), 221-226. 10.1017/S0004972700018694
Search in Google Scholar