Errata to ‘‘Vector measures and the strong operator topology”

A Strong Operator Topology Adiabatic Theorem

Spaces of Operator-valued Functions Measurable with Respect to the Strong Operator Topology

Let X and Y be Banach spaces and (Ω,Σ, μ) a finite measure space. In this note we introduce the space L[μ;L (X, Y )] consisting of all (equivalence classes of) functions Φ : Ω 7→ L (X, Y ) such that ω 7→ Φ(ω)x is strongly μ-measurable for all x ∈ X and ω 7→ Φ(ω)f(ω) belongs to L(μ; Y ) for all f ∈ L ′ (μ;X), 1/p + 1/p = 1. We show that functions in L[μ;L (X, Y )] define operator-valued measures...

Errata for Introduction to Symplectic Topology

This note corrects some typos and some errors in Introduction to Symplectic Topology (2nd edition, OUP 1998). In particular, in the latter book the statements of Theorem 6.36 (about Hamiltonian bundles) and Exercise 10.28 (about the structure of the group of symplectomorphisms of an open Riemann surface) need some modification. We thank everyone who pointed out these errors, and in particular K...

Continuity of Cp-semigroups in the Point-strong Operator Topology

We prove that if {φt}t≥0 is a CP-semigroup acting on a von Neumann algebra M ⊆ B(H), then for every A ∈ M and ξ ∈ H , the map t 7→ φt(A)ξ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CPsemigroups to semigroups of endomorphisms.

Locating subsets of B(H) relative to seminorms inducing the strong-operator topology

Let H be a Hilbert space, and A an inhabited, bounded, convex subset of B(H). We give a constructive proof that A is weak-operator totally bounded if and only if it is located relative to a certain family of seminorms that induces the strong-operator topology on B(H). 2000 Mathematics Subject Classification 03F60, 47S30 (primary)