The Mackey–Gleason–Bunce–Wright problem for vector-valued measures on projections in a $${\hbox {JBW}}^{*}$$-algebra
Year: 2026
Type: article
Abstract: Let $$\mathscr {P}(\mathfrak {J})$$ P ( J ) denote the lattice of projections of a $${\hbox {JBW}}^{*}$$ JBW ∗ -algebra $$\mathfrak {J}$$ J , and let X be a Banach space. A bounded finitely additive X -valued measure on $$\mathscr {P}(\mathfrak {J})$$ P ( J ) is a map $$\mu : \mathscr {P}(\mathfrak {J}) \rightarrow X$$ μ : P ( J ) → X satisfying ( a ) $$\mu (p +q) = \mu (p) + \mu (q)$$ μ ( p + q ) = μ ( p ) + μ ( q ) , whenever $$p \circ q = 0$$ p ∘ q = 0 in $$\mathscr {P}(\mathfrak {J})$$ P ( J ) , ( b ) $$\sup \{ \Vert \mu (p)\Vert : \, p \in \mathscr {P}(\mathfrak {J})\} < \infty $$ sup { ‖ μ ( p ) ‖ : p ∈ P ( J ) } < ∞ . In this paper we establish a Mackey–Gleason–Bunce–Wright theorem by showing that if $$\mathfrak {J}$$ J contains no type
Institution: Universidad de Granada
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
Awards: G1092424111, G1175115578, G1254525443, G1462035462, G2065685387, G21826877, G2193086574, G2262748287, G2420550025, G2720519961, G294895050, G300979063, G3099296600, G3252294556, G3480869486, G4045293325, G410571670, G425668148, G451917667, G4844356218, G4925834383, G5080475149, G523076202, G53827815, G5539308778, G567365627, G5967599077, G6033112984, G6384254145, G65626112, G6912840790, G6984395324, G7084143925, G7434936867, G7626972671, G8738026635, G9000352068
OpenAlex ID: W7203652906