On Statistical and Ideal Convergence of Sequences of Bounded Linear Operators

[1] M. Balcerzak, K. Dems, and A. Komisarski. Statistical convergence and ideal convergence
for sequences of functions, Journal of Mathematical Analysis and Applications, 328, 715–
729. 2007.
[2] V.K. Bhardwaj and I. Bala. On weak statistical convergence, International Journal of Mathematics
and Mathematical Sciences, Art. ID 38530, 9, 2007
[3] J. Connor. On strong matrix summability with respect to a modulus and statistical convergence,
Canadian Mathematical Bulletin, 32, 194–198. 1989.
[4] J. Connor. A topological and functional analytic approach to statistical convergence, Applied
and Numerical Harmonic Analysis, Birkhäuser Boston, Boston, MA, pp. 403–413.
[5] J. Connor, M. Ganichev, and V. Kadets. A characterization of Banach spces with separable
duals via weak statistical convergence, Journal ofMathematical Analysis and Applications,
244, 251–261. 2000.
[6] G. Di. Maio and Lj. D. R. Ko˘cinac. Statistical convergence in topology, Topology and its
Applications, 156, 28–45. 2008.
REFERENCES 366
[7] J. Fast. Sur la convergence statistique, Colloquium Mathematicum, 2, 241–244. 1951.
[8] A. R. Freedman. Generalized limits and sequence spaces, Bulletin of the London Mathematical
Society, 13, 224–228. 1981.
[9] A. R. Freedman and J. J. Sember. Densities and summability, Pacific Journal of Mathematics,
95, 293–305. 1981.
[10] J. A. Fridy and C. Orhan. Statistical limit superior and limit inferior, Proceedings of the
American Mathematical Society, 125, 3625–3631. 1997.
[11] H. Heuser. Funktionalanalysis, B. G. Teubner, Stuttgart, 1986.
[12] G. Kangro. On matrix transformations of sequences in Banach spaces, Izvestiya Akademii
Nauk Éstonskoi SSR. Seriya Tehnicheskikh i Fiziko-Matematicheskikh Nauk, 5, 108–128.
1956. (in Russian)
[13] E. Kolk. Statistically convergent sequences in normed spaces, Reports of conference "Methods
of Algebra and Analysis" (September 21–23, 1988, Tartu, Estonia), 63–66. 1988. (in
Russian)
[14] E. Kolk. The statistical convergence in Banach spaces, Tartu Ül. Toimetised, 928:41–52
1991.
[15] E. Kolk. Banach-Steinhaus type theorems for statistical and I -convergence with applications
to matrix maps, The Rocky Mountain Journal of Mathematics, 40, 279–289. 2010.
[16] P. Kostyrko, T. ˘Salát, and W. Wilczy´nski. I -convergence, Real Analysis Exchange, 26,
669–686. 2000/2001.
[17] G. Köthe. Topologische Lineare Räume. I, Die Grundlehren der Mathematischen Wissenschaften,
Band 107, Springer-Verlag, Berlin–Heidelberg–New York, 1966.
[18] I. E. Leonard. Banach sequence spaces, Journal ofMathematical Analysis and Applications,
54, 245–265. 1976.
[19] I.J. Maddox. Infinite Matrices of Operators, Lecture Notes in Mathematics 786, Springer-
Verlag, Berlin–Heidelberg–New York, 1980.
[20] I. J. Maddox. Statistical convergence in a locally convex space, Mathematical Proceedings
of the Cambridge Philosophical Society, 104, 141–145. 1988.
[21] S. Pehlivan, C. ¸Sençimen and Z. H. Yaman. On weak ideal convergence in normed spaces,
Journal of Interdisciplinary Mathematics, 13, 153–162. 2010.
[22] I. J. Schoenberg. The integrability of certain functions and related summability methods,
The American Mathematical Monthly, 66, 361–375. 1959.
REFERENCES 367
[23] H. Steinhaus. Sur la convergence ordinarie et la convergence asymptotique, Colloquium
Mathematicum, 2, 73–74. 1951.
[24] K. Zeller. VerallgemeinerteMatrixtransformationen,Mathematische Zeitschrift, 56, 18–20.
1952.
[25] A. Zygmund. Trigonometric Series, Cambridge University Press, Cambridge, 1979.