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On completely bounded bimodule maps over W*-algebras

Bojan Magajna (2003)

Studia Mathematica

It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type I ∞ , ∞ . Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map...

On Deddens΄s Theorem

S. Giotopoulos (1981)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On local automorphisms and mappings that preserve idempotents

Matej Brešar, Peter Šemrl (1995)

Studia Mathematica

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.

On multilinear generalizations of the concept of nuclear operators

Dahmane Achour, Ahlem Alouani (2010)

Colloquium Mathematicae

This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...

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