Spaceability in Banach Spaces Related to Locally Compact Groups

Authors
Dep. of Mathematics
Abstract
In this paper, for a locally compact group and a fixed number , we give some sufficient conditions for the set to be spaceable in . Also, by some special Segal algebras which recently have been introduced, we find spaceable subsets of the Fourier algebra . Finally, we give some necessary and sufficient conditions for a locally compact group to be compact or discrete.
Keywords

1. R. M. Aron, V.I. Gurariy and J.B. Seoane-Sepulveda, "Lineability and spaceability of sets of functions on R", Proc. Amer. Math. Soc. 133 (3) (2005), 795–803.

2. G. Botelho, D. Diniz, V.V. Fávaro, D. Pellegrino, "Spaceability in Banach and quasi-Banach sequence spaces", Linear Algebra Appl., 434 (5) (2011) 1255–1260.

3. G. Botelho, V.V. Fávaro, D. Pellegrino, J.B. Seoane-Sepúlveda , "L_p [0,1]⋃_(q>p)▒〖L_q [0,1]〗 is spaceable for every p > 0", Linear Algebra Appl., 436 (2012) 2963–2965.

4. H. G. Dales, "Banach Algebras and Automatic Continuity", Clarendon press, Oxford, 2000.

5. P. Eymard, "L’algèbre de Fourier d’un groupe localement compact", Bull. Soc. Math. France 92 (1964), 181–236.

6. V. P. Fonf, V. I. Gurariy and M. I. Kadets, "An infinite dimensional subspace of C[0,1] consisting of nowhere differentiable functions", C. R. Acad. Bulgare Sci. 52 (1999), 13–16.

7. F. Ghahramani and A.T.-M. Lau, "Weak amenability of certain classes of Banach algebras without bounded approximate identities", Math. Proc. Camb. Phil. Soc. (2002), 133, 357.

8. L. B. Gonzalez and M. O. Cabrera, "Spaceability of strict order integrability", J. Math. Anal. Appl. 385 (2012) 303–309.

9. V.I. Gurariy, L. Quarta, "On lineability of sets of continuous functions", J. Math. Anal. Appl., 294 (2004) 62–72.

10. J. Inoue and S.-E. Takahasi, "Segal algebras in commutative Banach algebras", Rocky Mountain J. Math. 44 (2014), no. 2, 539–589.

11. D. Kitson and R. M. Timoney, "Operator ranges and spaceability", J. Math. Anal. Appl. 378 (2011), 680–686.

12. M.G. Krein. "A principle of duality for bicompact groups and quadratic block algebras". Doklady

Akad. Nauk SSSR (N.S.) 69, (1949), 725-728.

13. W. Rudin, "Fourier Analysis on Groups", interscience publisher, Inc., New York, 1962.

14. W. Forrest Stinespring, "Integration theorems for gages and duality for unimodular groups", Trans. Amer. Math. Soc. 90 (1959), 15–56.

15. Y. Sawano and S. M. Tabatabaie, "Spaceability on Morrey spaces", submitted.

16. B. Subramanian, "On the inclusion L^p (μ)⊆L^q (μ)", Amer. Math. Monthly. 85 (1978), 479-481.

17. S. M. Tabatabaie and B. H. Sadathoseyni, "A spaceability result in the context of hypergroups",

Note Mat. 38 (1) (2018), 17–22.