On stability of classes of Lipschitz mappings generated by compact sets of linear mappings.
We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.
In the present paper we prove that a strictly cyclic, not invertible unicellular operator is quasinilpotent.
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].
We introduce and study a new concept of strongly -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 -summing if and only if its adjoint is -summing.
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.