Statistical Convergence and C*-operator Algebras

Gürdal Mehmet, Birgül Hubana Mualla

Abstract


In this article, we define in terms of Berezin symbols, reproducing kernels and statistical radial convergence the notion of generalized Engliš algebra, which is a C* -operator algebra on the Hardy space H2 (D) , and study its some properties.

 


Keywords


47B37, 40A35

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References


Berger, C.A and L.A Coburn (1986). Toeplitz operators and quantum mechanics. Journal of Functional Analysis 68(3), 273 – 299.

Berger, C.A. and L.A. Coburn (1987). Toeplitz operators on the Segal-Bargmann space. Transactions of the American Mathematical Society 301(2), 813–829.

Braha, N. L., H.M. Srivastava and S.A. Mohiuddine (2014). A Korovkins type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallee Poussin mean. Applied Mathematics and Computation 228(Supplement C), 162 – 169.

Douglas, R. (1972). Banach algebra techniques in operator theory. Academic Press, New York.

Englisš, M. (1995). Toeplltz operators and the Berezin transform on H2. Linear Algebra and its Applications 223- 224(Supplement C), 171 – 204. Honoring Miroslav Fiedler and Vlastimil Ptak.

Fridy, J.A. (1985). On statistical convergence. Analysis 5, 301–313.

Gurdal, M. and F. Sohret (2011). Some results for Toeplitz operators on the Bergman space. Applied Mathematics and Computation 218(3), 789 – 793. Special Issue in Honour of Hari M. Srivastava on his 70th Birth Anniversary.

Karaev, M.T. (2002). Berezin symbols and Schatten–von Neumann classes. Mathematical Notes 72(1), 185–192.

Karaev, M.T. (2004). Functional analysis proofs of Abel’s theorems. Proceedings of the American Mathematical

Society 132(8), 2327–2329.

Karaev, M.T. (2010). (e)-convergence and related problem. Comptes Rendus Mathematique 348(19), 1059 – 1062.

Mursaleen, M., F. Khan and A. Khan (2014). Statistical approximation for new positive linear operators of Lagrange type. Applied Mathematics and Computation 232(Supplement C), 548 – 558.

Nikolski, N.K. (1986). Treatise on the shift operator. Springer-Verlag, Berlin Heidelberg. Niven, I. and H.S. Zuckerman (1980). An Introduction to the Theorem of Numbers. New York.

Pehlivan, S. and M.T. Karaev (2004). Some results related with statistical convergence and Berezin symbols. Journal of Mathematical Analysis and Applications 299(2), 333 – 340.

Rudin, W. (1974). Real and Complex Analysis. Third ed. McGraw-Hili Book Co., Singapore.

Zhu, K. (1987). VMO, ESV and Toeplitz operators on the Bergman space. Transactions of the American Mathematical Society 302(2), 617–646.

Zhu, K. (1990). Operator Theory in Function Spaces. Mathematical Surveys and Monographs, Volume 138, AMS, United States of America.


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