Abstract
The process of differentiation is studied for a class of mappings of regions of a Hilbert space. We introduce the concept of ℂCl-differentiability of a mapping at a point and establish sufficient conditions of ℂCl-differentiability.
References
A. V. Bondar',Local Geometric Characteristics of Holomorphic Representations [in Russian], Naukova Dumka, Kiev (1992).
M. Krein, D. Milman, and M. Rutman, “On one property of bases in Banach spaces,”Zap.Nauch.-Issled. Inst. Mat. Mekh. Khark. Univ. Khark. Mat. Obshch.,16, 106–108 (1939).
V. É. Lyantse and O. G. Storozh,Methods of the Theory of Unbounded Operators [in Russian], Naukova Dumka, Kiev (1983).
T. Kato,Theory of Perturbations of Linear Operator [Russian translation], Mir, Moscow (1972).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 424–428, March, 1995.
Rights and permissions
About this article
Cite this article
Gretskii, O.S. ℂ-differentiability of mappings of Hilbert spaces. Ukr Math J 47, 494–499 (1995). https://doi.org/10.1007/BF01056315
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056315