Abstract
We present several generalizations of the classical Bari theorem on the Riesz basis property of close systems in Hilbert spaces to Banach spaces. We introduce the corresponding definitions and formulate theorems on the basis property of close systems in Banach spaces.
References
V. D. Mil’man, “Geometric theory of Banach spaces,” Usp. Mat. Nauk, 25, Issue 3, 113–174 (1970).
I. Zinger, Bases in Banach Spaces. I, Springer, Berlin (1970).
B. T. Bilalov, “Bases of exponents, cosines, and sines that are eigenfunctions of differential operators,” Differents. Uravn., 39, No. 5, 1–5 (2003).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 551–554, April, 2007.
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Bilalov, B.T., Muradov, T.R. On equivalent bases in Banach spaces. Ukr Math J 59, 615–619 (2007). https://doi.org/10.1007/s11253-007-0040-1
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DOI: https://doi.org/10.1007/s11253-007-0040-1