Maitland Wright - Academia.edu (original) (raw)

Uploads

Papers by Maitland Wright

Communications in Mathematical Physics, 1998

Gell-Mann and Hartle have proposed a significant generalisation of quantum theory in which decohe... more Gell-Mann and Hartle have proposed a significant generalisation of quantum theory in which decoherence functionals perform a key role. Verifying a conjecture of Isham-Linden-Schreckenberg, the author analysed the structure of bounded, finitely additive, decoherence functionals for a general von Neumann algebra A (where A has no Type I 2 direct summand). Isham et al. had already given a penetrating analysis for the situation where A is finite dimensional. The assumption of countable additivity for a decoherence functional may seem more plausible, physically, than that of boundedness. The results of this note are obtained much more generally but, when specialised to L(H), the algebra of all bounded linear operators on a separable Hilbert space H, give: Let d be a countably additive decoherence functional defined on all pairs of projections in L(H). If H is infinite dimensional then d must be bounded. By contrast, when H is finite dimensional, unbounded (countably additive) decoherence functionals always exist for L(H).

Bulletin of The London Mathematical Society, 1974

Let si be an arbitrary C*-algebra (with identity) and let A be the space of selfadjoint elements ... more Let si be an arbitrary C*-algebra (with identity) and let A be the space of selfadjoint elements of si. We recall that A is a partially ordered real vector space with positive cone {a*a: aesi}. If each upper bounded monotone increasing sequence in A has a least upper bound in A, then si is said to be monotone a-complete. It was shown in Wright [12] that each monotone <r-complete C*-algebra is the quotient of its Baire* envelope by a two-sided cr-ideal. It is proved here, in Theorem 3.5, that any C*-algebra si (with identity) can be embedded in a minimal monotone <7-complete C*-algebra and, further, the minimal c-completion of si is the quotient of the Baire* envelope of si by a certain two-sided c-ideal.

The Quarterly Journal of Mathematics, 1977

LET V be a boundedly complete vector lattice, or, in other words, a Dedekind complete Riesz space... more LET V be a boundedly complete vector lattice, or, in other words, a Dedekind complete Riesz space [2], . The object of this paper is to extend the main theorem of , which is a representation theorem for real valued states on Dini cones (see below for definitions), to a representation theorem for V -valued operators on Dini cones. In [13], Vincent-Smith showed by novel and elegant methods that an analogue of Choquet boundary theory can be developed for V -valued measures. As an application of our main theorem we are able to give an improved version of one of bis results.

MATHEMATICA SCANDINAVICA, 1989

Rendiconti Del Circolo Matematico Di Palermo, 1991

ABSTRACT

Pacific Journal of Mathematics, 1995

When A is a C*-algebra, a function d : A sa -» A sa is said to be a velocity map if, for each com... more When A is a C*-algebra, a function d : A sa -» A sa is said to be a velocity map if, for each commutative subalgebra B of A sa , d : B -> A sa is a derivation.

Quart J Math, 2009

We study weakly compact operators from a C * -algebra with values in a complete locally convex sp... more We study weakly compact operators from a C * -algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Saîto and Wright are extended to this more general setting. Building on an approach due to Saîto and Wright, we obtain our theorems on non-commutative finitely additive measures with values in a locally convex space, from more general results on weakly compact operators defined on Banach spaces X whose strong dual X is weakly sequentially complete. Weakly compact operators are also characterized by a continuity property for a certain "Right topology" as in joint work by Peralta, Villanueva, Wright and Ylinen. 2000 Mathematics Subject Classification. Primary: 47B07, secondary: 46L05, 46A03, 46A04, 47B48, 46L51.

Technometrics, 1984

The problem of process control in the presence of deterministic disturbances occurring rather inf... more The problem of process control in the presence of deterministic disturbances occurring rather infrequently, but at random intervals, is considered. It is shown that these processes can be represented by the same structural form of model as autoregressive-integrated-moving-average (ARIMA) processes, the only difference being in the probability distribution of the shocks. These models are useful in the important industrial problem

Matematicki Vesnik, 2012

In this note we show that weakly compact operators from a Banach space X into a complete (LB)-spa... more In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated.

J Math Anal Appl, 2004

Let B be a monotone σ-complete C∗-algebra. Let (μn) (n=1,2,…) be a sequence in the dual of B such... more Let B be a monotone σ-complete C∗-algebra. Let (μn) (n=1,2,…) be a sequence in the dual of B such that limμn(p) exists for each projection p. We prove that the sequence must converge weakly. As an application, we obtain a non-commutative generalisation of the Brooks–Jewett Theorem.

Let A be a C*-algebra. It is shown that A is an AW*-algebra if, and only if, each maximal abelian... more Let A be a C*-algebra. It is shown that A is an AW*-algebra if, and only if, each maximal abelian self-adjoint subalgebra of A is monotone complete. An analogous result is proved for Rickart C*-algebras; a C*-algebra is a Rickart C*-algebra if, and only if, it is unital and each maximal abelian self-adjoint subalgebra of A is monotone σ−complete.

Proceedings of the London Mathematical Society, 2013

Quarterly Journal of Mathematics, 2010

Schaefer and Zhang have recently obtained an analogue, for se- quentially order continuous functi... more Schaefer and Zhang have recently obtained an analogue, for se- quentially order continuous functionals on C(K), of a much earlier theorem of Dixmier. In this note it is shown that the Schaefer-Zhang Theorem has a natural generalisation to non-commutative C-algebras. These results are obtained as consequences of our main theorem which is concerned with ane functions on compact convex sets.

Pacific Journal of Mathematics, 1996

Let A be a C*-algebra with no quotient isomorphic to the algebra of all two-by-two matrices. Let ... more Let A be a C*-algebra with no quotient isomorphic to the algebra of all two-by-two matrices. Let μ be a quasi-linear functional on A. Then μ is linear if, and only if, the restriction of μ to the closed unit ball of A is uniformly weakly continuous.