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Representations of bimeasures

Kari Ylinen (1993)

Studia Mathematica

Separately σ-additive and separately finitely additive complex functions on the Cartesian product of two algebras of sets are represented in terms of spectral measures and their finitely additive counterparts. Applications of the techniques include a bounded joint convergence theorem for bimeasure integration, characterizations of positive-definite bimeasures, and a theorem on decomposing a bimeasure into a linear combination of positive-definite ones.

Representations of the direct product of matrix algebras

Daniele Guido, Lars Tuset (2001)

Fundamenta Mathematicae

Suppose B is a unital algebra which is an algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and the σ-complete ultrafilters on X (Theorem 2.6). Therefore, if X has less than measurable cardinality (e.g. accessible), the equivalence classes of the irreducible representations of B are labeled by points of X, and all representations of B are described (Theorem 3.3).

Representations of the spaces C ( N ) H k , p ( N )

A. Albanese, V. Moscatelli (2000)

Studia Mathematica

We give a representation of the spaces C ( N ) H k , p ( N ) as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that C ( N ) H k , 2 ( N ) is isomorphic to the sequence space s l 2 ( l 2 ) , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

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