Annals of Functional Analysis

On generalized weighted means and compactness of matrix operators

Ali Karaisa

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This paper mainly divided into two parts. The first part gives same facts about topological properties of certain linear topological spaces, inclusion relations and matrix mappings. The second part establishes some identities or estimates for the matrix operator norms and the Hausdorff measures of noncompactness of certain matrix operators, characterize some classes of compact operators on these spaces.

Article information

Ann. Funct. Anal., Volume 6, Number 3 (2015), 8-28.

First available in Project Euclid: 17 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45]
Secondary: 40H05: Functional analytic methods in summability 40C05: Matrix methods

BK-space compactness generalized weighted mean matrix operator


Karaisa, Ali. On generalized weighted means and compactness of matrix operators. Ann. Funct. Anal. 6 (2015), no. 3, 8--28. doi:10.15352/afa/06-3-2.

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  • A. Sönmez and F. Başar, Generalized Diffrence space on none-absolute type of convergent and null sequences, Abstr. Appl. Anal. 2012 Article ID 435076 (2012) 1–20.
  • A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies 85, Amsterdam-New York-Oxford, 1984.
  • B. Altay and F. Başar, On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26(5) (2003) 701–715
  • F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs \.Istanbul, 2012.
  • F. Başar and A. Karaisa, Some new generalized difference spaces of nonabsolute type derived from the spaces $\ell_{p}$ and $\ell_{\infty}$, The Scientific World Journal 2013 Article ID 349346 2013 doi:10.1155/2013/349346 1–15.
  • A. Karaisa, Hausdorff measure of noncompactness in some sequence space of a triple band matrix J. Inequal. App. 2013, 2013:503, 11 pp.
  • C. Ayd\i n and F. Başar, Some new diference sequence spaces, Appl. Math. Comput. 154(2004) 677–693.
  • E. Malkowsky and V. Rakočević, On matrix domains of triangles, Appl. Math. Comput. 189, no. 2, (2007) 1146–1163.
  • E. Malkowsky and V. Rakočević, An introduction into the theory of sequence spaces and measures of noncompactness Zbornik Mat. institut sanu (Beograd)radova 9 (2000), no. 17, 143–34.
  • H. Nakano, Modulared sequence spaces Proc. Japan Acad. 27 (1951) 508–512.
  • K.G. Grosse-Erdmann, Matrix transformations between the sequence spaces of Maddox J. Math. Anal. Appl. 180(1993) 223–238.
  • F. Özger and F. Başar, Domain of the double sequential band matrix $B(r,s)$ on some Maddox's spaces, Acta Math.Sci. 34 (2014), no. 2, 394–408.
  • E. Malkowsky and F. Özger, A note on some sequence spaces of weighted means, Filomat 26 (2012), no. 3, 511–518.
  • M. Mursaleen and A.K. Noman, Applications of the Hausdorff measure of noncompactness in some sequence spaces of weighted means Comput. Math. Appl. 60 (2010) 1245–125.
  • M. Mursaleen and A.K. Noman, Compactness of matrix operators on some new difference sequence spaces, Linear Algebra Appl. 436 (2012) 41–52.
  • A.M. Jarrah and E. Malkowsky, BK spaces, bases and linear operators Rendiconti Circ. Mat. Palermo II 52 177–191 (1990).
  • M. Mursaleen and A.K. Noman, Compactness by the Hausdorff measure of noncompactness Nonlinear Anal. 73 (2010) 2541–2557.
  • I.J. Maddox, Elements of Functional Analysis, $2$nd ed. The University Press Cambridge, (1988).
  • J. Boos, Oxford University Press Inc, New York Classical and Modern Methods in Summability Oxford University Press Inc, New York 2000.
  • S. Simons, The sequence spaces $\ell(pv)$ and $m(pv)$ Proc. London Math. Soc. (3) 15 (1965), no. 1, 422–36.
  • A. Karaisa and Ü. Karab\iy\ik, Almost sequence spaces derived by the domain of the matrix, Abstr. Appl. Anal. 2013 Article ID 783731 (2013) 1–8.
  • I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc. 64(1968) 335–340.
  • V. Karakaya, A.K. Noman and H. Polat, On paranormed $\lambda$-sequence spaces of non-absolute type, Math. Comput. Modelling 54 (2011) 1473–480.