Compact weighted endomorphisms of $C(X)$

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Compact endomorphisms of H ∞ (D)

Let D be the open unit disc and, as usual, let H(D) be the algebra of bounded analytic functions on D with ‖f‖ = supz∈D |f(z)|. With pointwise addition and multiplication, H(D) is a well known uniform algebra. In this note we characterize the compact endomorphisms of H(D) and determine their spectra. We show that although not every endomorphism T of H(D) has the form T (f)(z) = f(φ(z)) for some...

Endomorphisms of Compact Abelian Groups Minimize Entropy

The entropy conjecture for tori has been settled a long time ago by Misiurewicz and Przytycki. We show that their result extends from tori to compact and connected abelian groups. We give stronger results for hyperbolic automorphisms. Throughout this paper G denotes a compact and connected metric abelian group. The group operation on G is written additively.

compact endomorphisms of certain subalgebras of the disk algebra

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.