6 papers
Invariant subspaces and Deddens algebras
Miguel Lacruz
It is shown that if the Deddens algebra associated with a quasinilpotent operator on a complex Banach space is closed and localizing then has a nontrivial…
Extended eigenvalues for Cesàro operators
Miguel Lacruz, Fernando León-Saavedra, John Petrovic +1
A complex scalar is said to be an extended eigenvalue of a bounded linear operator on a complex Banach space if there is a nonzero operator such that Such an…
Localizing algebras and invariant subspaces
Miguel Lacruz, Luis Rodríguez-Piazza
It is shown that the algebra \(L^\infty(μ)\) of all bounded measurable functions with respect to a finite measure \(μ\) is localizing on the Hilbert space \(L^2(μ)\) if and only if…
Applications of fixed point theorems in the theory of invariant subspaces
Rafa Espínola, Miguel Lacruz
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the exi…
Hardy-Littlewood inequalities for norms of positive operators on sequence spaces
Miguel Lacruz
We consider estimates of Hardy and Littlewood for norms of operators on sequence spaces, and we apply a factorization result of Maurey to obtain improved estimates and simplified p…
A local spectral condition for strong compactness with some applications to bilateral weighted shifts
Miguel Lacruz, Maria del Pilar Romero de la Rosa
An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear o…