Spaces of sigma(p)-nuclear linear and multilinear operators on Banach spaces and their duals

作者：Botelho Geraldo; Mujica Ximena^*

来源：Linear Algebra and Its Applications, 2017, 519: 219-237.

DOI：10.1016/j.laa.2017.01.002

• sigma(p)-nuclear operators
• Quasi-tau(p)-summing operators
• Duality
• Borel transform

The theory of tau-summing and a-nuclear linear operators on Banach spaces was developed by Pietsch [20, Chapter 23]. Extending the linear case to the range p > 1 and generalizing all cases to the multilinear setting, in this paper we introduce the concept of sigma(p)-nuclear linear and multilinear operators. In order to develop the duality theory for the spaces of such operators, we introduce the concept of quasi-tau(p)-summing linear/multilinear operators and prove Pietsch-type domination theorems for such operators. The main result of the paper shows that, under usual conditions, linear functionals on the space of a(p)-nuclear n-linear operators are represented, via the Borel transform, by quasi-tau(p)-summing n-linear operators. As far as we know, this result is new even in the linear case n = 1.

• 出版日期2017-4-15