ON PROPER EXPANSIONS AND PROPER CONTRACTIONS OF NONLINEAR OPERATORS REPRESENTED IN THE FORM OF A PRODUCT
Shynybekov A.
30 September 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#127Issue 33 - 10 pp.
Today there are many works devoted to the questions of expansion and contraction of operators [1–12]. In all these works the questions of expansion of the additive “minimal” operator and the questions of contraction of the additive “maximal” operator are considered. In this paper it is shown that these restrictions on the additivity of the corresponding operators are not essential. In [10] the questions of proper contraction of a maximal operator represented as a product are considered, i.e., the relationship between the set of proper contractions of the operator A = LM and the sets of proper contractions of the operators L and M is established. Here, an abstract theorem is proved which allows us to establish the relationship between the set of proper extensions of the operator A0 = L0 M0 and the sets of proper extensions of the operators L0 and M0. In this connection, we prove an abstract theorem that allows us to describe the correct contractions of one class of nonlinear operators represented as a product.
Bitsadze-Samarskii type problem , correct contraction , correct expansion , operator , regular expansion
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Al-Farabi Kazakh national university, Almaty, Kazakhstan
Al-Farabi Kazakh national university
10 лет помогаем публиковать статьи Международный издатель
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