Compactness of quadruple band matrix operator and geometric properties

Authors

  • Mustafa Cemil Bişgin Recep Tayyip Erdogan University, Mathematics
  • Abdulcabbar Sönmez Erciyes University, Department of Mathematics

Keywords:

matrix transformations, matrix domain, compact operators, Hausdorff measure of noncompactness, matrix classes

Abstract

In this work, we characterize the class of compact matrix operators from c0(Q), c(Q) and l(Q) into c0, c and l, respectively, with the notion of the Hausdorff measure of noncompactness. Moreover, we determine some geometric properties of the sequence space lp(Q).

References

Ahmad, Zaheer U., and Mohammad Mursaleen. "Köthe-Toeplitz duals of some new sequence spaces and their matrix maps." Publ. Inst. Math. (Beograd) (N.S.) 42(56) (1987): 57-61.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Asma, Çigdem, and Rifat Çolak. "On the Köthe-Toeplitz duals of some generalized sets of difference sequences." Demonstratio Math. 33, no. 4 (2000): 797–803.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Basarir, Metin, and Mustafa Kayikçi. "On the generalized Bm-Riesz difference sequence space and β-property." J. Inequal. Appl. 2009 (2009): Art. ID 385029, 18 pp.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Beauzamy, Bernard. "Banach-Saks properties and spreading models." Math. Scand. 44, no. 2 (1979): 357-384.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Bektas, Çigdem A. "On some new generalized sequence spaces." J. Math. Anal. Appl. 277, no. 2 (2003) 681-688.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Bisgin, Mustafa Cemil. "Four new sequence spaces obtained from the domain of quadruple band matrix operator." Under Review.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Bisgin, Mustafa Cemil. "Almost convergent sequence spaces derived by the domain of quadruple band matrix." Ann. Univ. Paedagog. Crac. Stud. Math. 19 (2020): 155-170.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Choudhary, Bishweshwar, and Sudarsan Nanda. Functional Analysis with Applications. New York: John Wiley & sons Inc., 1989.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Demiriz, Serkan, and Emrah Evren Kara. "On compact operators on some sequence spaces related to matrix B(r, s, t)." Thai J. Math. 14, no. 3 (2016): 651-666.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Djolovic, Ivana. "On compact operators on some spaces related to matrix B(r, s)." Filomat 24, no. 2 (2010): 41-51.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Djolovic, Ivana, and Eberhard Malkowsky. "A note on compact operators on matrix domains." J. Math. Anal. Appl. 340, no. 1 (2008): 291-303.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Djolovic, Ivana, and Eberhard Malkowsky. "Matrix transformations and compact operators on some new mth-order difference sequences." Appl. Math. Comput. 198, no. 2 (2008): 700-714.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Et, Mikail. "On some difference sequence spaces." Doga Mat. 17, no. 1 (1993): 18-24.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Et, Mikail, and Rıfat Çolak. "On some generalized difference sequence spaces." Soochow J. Math. 21, no. 4 (1995): 377-386.
##plugins.generic.googleScholarLinks.settings.viewInGS##

García-Falset, Jesús. "Stability and fixed points for nonexpansive mappings." Houston J. Math. 20, no. 3 (1994): 495-506.
##plugins.generic.googleScholarLinks.settings.viewInGS##

García-Falset, Jesús. "The fixed point property in Banach spaces with the NUSproperty." J. Math. Anal. Appl. 215, no. 2 (1997): 532-542.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Jarrah, Abdullah M., and Eberhard Malkowsky. "Ordinary, absolute and strong summability and matrix transformations." Filomat 17 (2003): 59-78.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Kirisçi, Murat, and Feyzi Basar, "Some new sequence spaces derived by the domain of generalized difference matrix." Comput. Math. Appl. 60, no. 5 (2010): 1299-1309.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Kızmaz, Hüsnü. "On certain sequence spaces." Canad. Math. Bull. 24, no. 2, (1981): 169-176.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Knaust, Helmut. "Orlicz sequence spaces of Banach-Saks type." Arch. Math. (Basel) 59, no. 6 (1992): 562-565.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Maddox, Ivor J. Elements of functional analysis. Cambridge: Cambridge University Press (2nd edition), 1988.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Malkowsky, Eberhard, and Vladimir Rakocevic. "On matrix domains of triangles." Appl. Math. Comput. 189, no. 2 (2007): 1146-1163.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Malkowsky, Eberhard, and Vladimir Rakocevic. "An introduction into the theory of sequence spaces and measures of noncompactness." Zb. Rad. (Beogr.) 9(17) (2000): 143-234.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Malkowsky, Eberhard, and Vladimir Rakocevic, and Orhan Tuˇg. "Compact operators on the Hahn space." Monatsh. Math. 196, no. 3 (2021): 519-551.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Malkowsky, Eberhard, et al. "The roots of polynomials and the operator Δ3i on the Hahn sequence space h." Comput. Appl. Math. 40, no. 6 (2021): Paper No. 222, 18 pp.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Mursaleen, Mohammad. "Generalized spaces of difference sequences." J. Math. Anal. Appl. 203, no. 3, (1996): 738-745.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Rakocevic, Vladimir. "Measures of noncompactness and some applications." Filomat 12, part 2 (1998): 87-120.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Sánchez, Luisa, and Antonio Ullán. "Some properties of Gurarii’s modulus of convexity." Arch. Math. (Basel) 71, no. 5 (1998): 399-406.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Sönmez, Abdulcabbar. "Some new sequence spaces derived by the domain of the triple band matrix." Comput. Math. Appl. 62, no. 2, (2011): 641-650.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Tuˇg, Orhan, and Vladimir Rakocevic, and Eberhard Malkowsky. "Domain of generalized difference operator Δ3i of order three on the hahn sequence space
##plugins.generic.googleScholarLinks.settings.viewInGS##

h and matrix transformations." Linear and Multilinear Algebra (2021): DOI: 10.1080/03081087.2021.1991875.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Tuˇg, Orhan. "The generalized difference operator Δ3i of order three and its domain in the sequence spaces l1 and bv." J. Math. 2022 (2022): Art. ID 6343084, 13 pp.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Wilansky, Albert. Summability through functional analysis. Vol. 85 of North-Holland Mathematics Studies. Amsterdam: North-Holland Publishing Co., 1984.
##plugins.generic.googleScholarLinks.settings.viewInGS##

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Published

2022-08-29

How to Cite

Bişgin, M. C., & Sönmez, A. (2022). Compactness of quadruple band matrix operator and geometric properties. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 21, 17–32. Retrieved from https://studmath.uken.krakow.pl/article/view/9488

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