7,732 research outputs found
Open problems in Banach spaces and measure theory
We collect several open questions in Banach spaces, mostly related to measure
theoretic aspects of the theory. The problems are divided into five categories:
miscellaneous problems in Banach spaces (non-separable spaces,
compactness in Banach spaces, -null sequences in dual spaces),
measurability in Banach spaces (Baire and Borel -algebras, measurable
selectors), vector integration (Riemann, Pettis and McShane integrals), vector
measures (range and associated spaces) and Lebesgue-Bochner spaces
(topological and structural properties, scalar convergence)
Simultaneous universality
In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint universality. Several criteria are provided, and several applications to specific operators or sequences of operators are performed, mainly in the setting of sequence spaces or spaces of holomorphic functions.Plan Andaluz de Investigación (Junta de AndalucÃa)Ministerio de EconomÃa y CompetitividadDeutsche Forschungsgemeinschaf
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