Additive iterative roots of identity and Hamel bases

作者：Jablonski Wojciech^*

来源：Aequationes Mathematicae, 2016, 90(1): 133-145.

DOI：10.1007/s00010-015-0376-9

• Additive function
• Hamel base
• Babbage's equation
• Iterative root

We describe a class of discontinuous additive functions a : X -> X on a real topological vector space X such that a(n) = id(X) and a(H)\H not equal empty set for every infinite set H subset of X of vectors linearly independent over Q. We prove the density of the family of all such functions in the linear topological space A(X) of all additive functions a : X. X with the topology induced on A(X) by the Tychonoff topology of the space X-X. Moreover, we consider additive functions a is an element of A(X) satisfying a(n) = id(X) and a(H) = H for some Hamel basis H of X. We show that the class of all such functions is also dense in A(X). The method is based on decomposition theorems for linear endomorphisms.

• 出版日期2016-2