A space on which diameter-type packing measure is not Borel regular

A Pseudocompact Completely Regular Frame which is not Spatial

Compact regular frames are always spatial. In this note we present a method for constructing non-spatial frames. As an application we show that there is a countably compact (and hence pseudocompact) completely regular frame which is not spatial.

Bisimilarity is not Borel

We prove that the relation of bisimilarity between countable labelled transition systems is Σ1-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and nondeterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the...

A not on modular hyperconvex space

A Polynomially Bounded Operator on Hilbert Space Which Is Not Similar to a Contraction

Let ε > 0. We prove that there exists an operator Tε : `2 → `2such that for any polynomial P we have ‖P (Tε)‖ ≤ (1 +ε)‖P‖∞, but Tε isnot similar to a contraction, i.e. there does not exist an invertible operatorS : `2 → `2 such that‖S−1TεS‖ ≤ 1. This answers negatively a question at-tributed to Halmos after his well-known 1970 paper (“Ten problems in Hilbertspace”). ...

Borel measurable functionals on measure algebras

For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...