Duals of Vector valued Function Spaces $c_0(X,U,M)$, $c(X,U,M)$ and $l_\infty}(X,U,M)$ defined by Orlicz Function
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Abstract
In this paper we obtain the K\"othe-Toeplitz duals of ${c_0}(X,U,M)$, $c (X, U, M)$ and ${l_\infty }(X, U, M)$. We extend the definition of Maddox and study of function spaces and sequence spaces defined also by Orlicz function. Further we characterize the continuous dual of ${c_0}(X,U,M)$ and $c (X, U, M)$.
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Yadav, Y., & Srivastava, J.
(2014).
Duals of Vector valued Function Spaces $c_0(X,U,M)$, $c(X,U,M)$ and $l_\infty}(X,U,M)$ defined by Orlicz Function.
Acta Mathematica Universitatis Comenianae, 83(1), 29-38.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/73/52
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References
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[9] Yilmaz, Yilmaz, Ozdemir, M. Kemal : Kothe-Toeplitz duals of some vector valued Orlicz sequence spaces, Soochow Jour. of Mathematics, 31 No. 3 (2005), 389-402.
[10] Yilmaz, Y., Ozdemir, K., Solak, _I. and Candan, M. : Operators on some vector valued Orlicz sequence spaces, Firat Universitesi Fen Bilimleri Enstitusu, Fen ve Muhendislik Bilimleri Dergisi, C.17, S.1, 2005.
[2] Horvath, J. : Topological vector spaces and distributions, Vol. I, Addison Wesley (1966).
[3] Kolk, E. : Topologies in generalized Orlicz sequence spaces, Filomat, 25 : 4 (2011), 191-211.
[4] Lidenstrauss, J. and Tzafriri, L. : Classical Banach spaces I, Sequence spaces, Springer Verlag, New York, Berlin (1977).
[5] Parashar, S. D. and Chaoudhary, B. : Sequence spaces dened by Orlicz functions, Indian J. Pure Appl. Math., 25 (4) (1994), 419-428.
[6] Savas, E. and Pattersan, F. : An Orlicz extension of some new sequence spaces dened by Orlicz functions, Thai J. of Mathematics, 3 No. 2 (2005), 209-218.
[7] Srivastava, J. K. and Tiwari, R. K. : On certain Banach space valued function spaces-I, Math. Forum, 20 (2007-08), 14-31.
[8] Srivastava, J. K. and Yadav, Y. : Vector valued function spaces c0(X; U;M), c(X; U;M) and l1(X; U;M) dened by Orlicz function, J. Raj. Acad. Phy. SCi., 11 No. 3 (2012).
[9] Yilmaz, Yilmaz, Ozdemir, M. Kemal : Kothe-Toeplitz duals of some vector valued Orlicz sequence spaces, Soochow Jour. of Mathematics, 31 No. 3 (2005), 389-402.
[10] Yilmaz, Y., Ozdemir, K., Solak, _I. and Candan, M. : Operators on some vector valued Orlicz sequence spaces, Firat Universitesi Fen Bilimleri Enstitusu, Fen ve Muhendislik Bilimleri Dergisi, C.17, S.1, 2005.