A Note On The Series Space ?? ? ? ??(?)

The series space ?? ? ? ? ?(?) has recently been introduced and studied by Gökçe and Sarıgöl [1]. The main purpose of this paper is to determine the ? −, ? − and ? −duals of the space ?? ? ? ? ?(?) and to show that it is linearly isomorphic to the Maddox’s space ?(?).

PDF

___

F. Gökçe and M.A. Sarıgöl, “A new series space ?? ? ? ? ?(?) and matrix operator with applications”, Kuwait Journal of Science, vol. 45, no. 4, pp. 1-8, 2018

I. J. Maddox, “Some properties of paranormed sequence spaces,” Journal of the London Mathematical Society, vol. 1, pp. 316–322, 1969.

I. J. Maddox, “Paranormed sequence spaces generated by infinite matrices,”Mathematical Proceedings of the Cambridge Philosophical Society, vol. 64, pp. 335–340, 1968.

I.J. Maddox, “Spaces of strongly summable sequences,” The Quarterly Journal of Mathematics, vol. 18, no. 1, pp. 345–355, 1967.

H. Bor, “On |? ? , ??|? summability factors of infinite series,” Tamkang Journal of Mathematics, vol. 16, pp. 13– 20, 1985.

T.M. FLett, “On an extension of absolute summability and some theorems of Littlewood and Paley,” Proceedings of the London Mathematical Society, vol.3, no.1, pp. 113-141, 1957.

M.A. Sarıgöl, “Spaces of series summable by absolute Cesàro and matrix operators,” Communications in Mathematics and Appliations, vol. 7, no.1, pp. 11–22, 2016.

M.A. Sarıgöl, “Norms and compactness of operators on absolute weighted mean, summable series,” Kuwait Journal of Science, vol. 43, no. 4, pp. 68–74, 2016.

M.A. Sarıgöl, “An inequality for matrix operators and its applications.,” Journal of Classical Analysis, vol. 2, no.2, pp. 145–150, 2013.

M.A. Sarıgöl, “Matrix transformations on fields of absolute weighted mean summability,” Studia Scientiarum Mathematicarum Hungarica, vol. 48, no. 3, pp. 331–341, 2011.

M.A. Sarıgöl, “On local properties of factored Fourier series.” Applied Mathematics and Computation, vol. 216, no. 11, pp. 3386–3390, 2010.

K.G. Grosse-Erdmann, “Matrix transformations between the sequence spaces of Maddox,” Journal of Mathematical Analysis and Applications, vol. 180, pp. 223– 238, 1993.