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- Teresa Bermúdez
- 2002

We prove that for every bounded linear operator T : X → X, where X is a non-reflexive quotient of a von Neumann algebra, the point spectrum of T ∗ is non-empty (i.e. for some λ ∈ C the operator λI − T fails to have dense range.) In particular, and as an application, we obtain that such a space cannot support a topologically transitive operator.

- Teresa Bermúdez, AntonioMartinón VladimírMüller, Juan Agustín Noda, Teresa Bermúdez, Antonio Martinón
- 2014

We prove that if T is an m-isometry on a Hilbert space and Q an n-nilpotent operator commuting with T , then T + Q is a (2n + m− 2)-isometry. Moreover, we show that a similar result for (m, q)-isometries on Banach spaces is not true.

- Teresa Bermúdez, Antonio Martinón
- Appl. Math. Lett.
- 2011

We consider ideals I of subsets of the set of natural numbers N such that for every conditionally convergent series of real numbers ∑ n∈N an and s ∈ R, then there is a sequence of signs δ = (δn)n∈N such that ∑ n∈N δnan = s and N(δ) := {n ∈ N : δn = −1} ∈ I. We give some properties of such ideals and characterize them in terms of extendability to a summable… (More)

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