The Semilattices with Distinguished Endomorphisms which are Equationally Compact

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Uniform endomorphisms which are isomorphic to a Bernoulli shift

A uniformly p-to-one endomorphism is a measure-preserving map with entropy log p which is almost everywhere p-to-one and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is a one-sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by ...

Uniform Endomorphisms Which Are Isomorphic to a Bernoulli Shift

A uniformly p to one endomorphism is a measure preserving map with entropy log p which is a.e. p to 1 and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is one sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite to one endomorphisms conjugate to this standard example by a condition on th...

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...

compact endomorphisms of certain subalgebras of the disk algebra