The solvability of the equation A(x) = f(x) on the sphere of a Hilbert space and the dimension of its solution set are studied in the case where A is a closed surjective operator and f is an odd Lipschitz mapping. A kind of analogue of the infinite-dimensional version of the Borsuk-Ulam theorem is obtained.

中文翻译：

---

无限维空间上Lipschitz映射的Borsuk-Ulam定理

在A是封闭的射影算子且f是奇数Lipschitz映射的情况下，研究了方程A（x）= f（x）在希尔伯特空间球面上的可解性及其解集的维数。获得了Borsuk-Ulam定理的无穷维形式的一种类似物。