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Featured researches published by P. G. Dodds.


Transactions of the American Mathematical Society | 1993

Noncommutative Köthe duality

P. G. Dodds; Theresa K.-Y. Dodds; Ben de Pagter

Using techniques drawn from the classical theory of rearrangement invariant Banach function spaces we develop a duality theory in the sense of Kothe for symmetric Banach spaces of measurable operators affiliated with a semifinite von Neumann algebra equipped with a distinguished trace. A principal result of the paper is the identification of the Kothe dual of a given Banach space of measurable operators in terms of normality


Integral Equations and Operator Theory | 1992

Fully symmetric operator spaces

P. G. Dodds; Theresa K.-Y. Dodds; Ben de Pagter

It is shown that certain interpolation theorems for non-commutative symmetric operator spaces can be deduced from their commutative versions. A principal tool is a refinement of the notion of Schmidt decomposition of a measurable operator affiliated with a given semi-finite von Neumann algebra.


Positivity | 1998

Symmetric Functionals and Singular Traces

P. G. Dodds; B. de Pagter; E. M. Semenov; Fedor Sukochev

We study the construction and properties of positive linear functionals on symmetric spaces of measurable functions which are monotone with respect to submajorization. The construction of such functionals may be lifted to yield the existence of singular traces on certain non-commutative Marcinkiewicz spaces which generalize the notion of Dixmier trace.


Transactions of the American Mathematical Society | 1996

CHARACTERIZATIONS OF KADEC-KLEE PROPERTIES IN SYMMETRIC SPACES OF MEASURABLE FUNCTIONS

V. I. Chilin; P. G. Dodds; A. A. Sedaev; Fyodor Sukochev

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the K-functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.


Journal of Functional Analysis | 1985

Spectral measures and the Bade reflexivity theorem

P. G. Dodds; Werner J. Ricker

Let B be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by B in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed B-invariant subspace of X.


arXiv: Functional Analysis | 1995

A uniform Kadec-Klee property for symmetric operator spaces

P. G. Dodds; Theresa K.-Y. Dodds; Paddy N. Dowling; Chris Lennard; Fedor Sukochev

We show that if a rearrangement invariant Banach function space E on the positive semi-axis satisfies a non-trivial lower q -estimate with constant 1 then the corresponding space E (M) of τ-measurable operators, affiliated with an arbitrary semi-finite von Neumann algebra M equipped with a distinguished faithful, normal, semi-finite trace τ, has the uniform Kadec-Klee property for the topology of local convergence in measure. In particular, the Lorentz function spaces L q, p and the Lorentz-Schatten classes C g, p have the UKK property for convergence locally in measure and for the weak-operator topology, respectively. As a partial converse, we show that if E has the UKK property with respect to local convergence in measure then E must satisfy some non-trivial lower q -estimate. We also prove a uniform Kadec-Klee result for local convergence in any Banach lattice satisfying a lower q -estimate.


Israel Journal of Mathematics | 1997

THE KADEC-KLEE PROPERTY IN SYMMETRIC SPACES OF MEASURABLE OPERATORS

V. I. Chilin; P. G. Dodds; Fedor Anatol'evich Sukochev

We show that ifE is a separable symmetric Banach function space on the positive half-line thenE has the Kadec-Klee property if and only if, for every semifinite von Neumann algebra (M, τ), the associated spaceE(M, τ) ofτ-measurable operators has the Kadec-Klee property.


Mathematical Proceedings of the Cambridge Philosophical Society | 2001

Weak compactness criteria in symmetric spaces of measurable operators

Fyodor Sukochev; G. Schluchtermann; P. G. Dodds

The principal result of the paper reduces the study of certain weakly compact sets in Banach spaces of measurable operators to that of the corresponding sets of generalized singular value functions. In particular, under natural conditions, it is shown that the orbit of a relatively weakly compact subset of the Kothe dual of a symmetric space of measurable operators affiliated with some semi-finite von Neumann algebra is again relatively weakly compact.


Operator theory | 1995

On a Submajorization Inequality of T. Ando

P. G. Dodds; Theresa K.-Y. Dodds

A submajorization inequality of T.Ando for operator monotone functions is extended to the setting of measurable operators affiliated with a semi-finite von Neumann algebra. The general form yields certain norm inequalities for the absolute value in symmetric operator spaces which were previously known in the setting of trace ideals.


Mathematical Proceedings of the Cambridge Philosophical Society | 1991

Weakly compact subsets of symmetric operator spaces

P. G. Dodds; Theresa K.-Y. Dodds; Ben de Pagter

Under natural conditions it is shown that the rearrangement invariant hull of a weakly compact subset of a properly symmetric Banach space of measurable operators affiliated with a semi-finite von Neumann algebra is again relatively weakly compact.

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B. de Pagter

Delft University of Technology

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Fedor Sukochev

University of New South Wales

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E. M. Semenov

Voronezh State University

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Ben de Pagter

Delft University of Technology

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Anton R. Schep

University of South Carolina

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Werner J. Ricker

University of New South Wales

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