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On strong generation of B(ℋ) by two commutative C*-algebras

R. Berntzen, A. Sołtysiak (1997)

Studia Mathematica

The algebra B(ℋ) of all bounded operators on a Hilbert space ℋ is generated in the strong operator topology by a single one-dimensional projection and a family of commuting unitary operators with cardinality not exceeding dim ℋ. This answers Problem 8 posed by W. Żelazko in [6].

On strongly l p -summing m-linear operators

Lahcène Mezrag (2008)

Colloquium Mathematicae

We introduce and study a new concept of strongly l p -summing m-linear operators in the category of operator spaces. We give some characterizations of this notion such as the Pietsch domination theorem and we show that an m-linear operator is strongly l p -summing if and only if its adjoint is l p -summing.

On strongly stable approximations.

F. Arandiga, V. Caselles (1994)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we prove that the convergence of (T - Tn)Tn-k to zero in operator norm (plus some technical conditions) is a sufficient condition for Tn to be a strongly stable approximation to T, thus extending some previous results existing in the literature.

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