We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69–87, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem.
Castellano, I., Giordano Bruno, A. (2017). Algebraic entropy in locally linearly compact vector spaces. In M. Fontana, S. Frisch, S. Glaz, F. Tartarone, P. Zanardo (a cura di), Rings, Polynomials, and Modules (pp. 103-127). Springer International Publishing [10.1007/978-3-319-65874-2_6].
Algebraic entropy in locally linearly compact vector spaces
Castellano, I;
2017
Abstract
We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69–87, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem.
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