5 papers · 1 filter
Summing inclusion maps between symmetric sequence spaces
Andreas Defant, Mieczysław Mastyło, Carsten Michels
We prove a substantial extension of a well-known result due to Bennett and Carl: The inclusion of a 2-concave symmetric Banach sequence space E into l_2 is (E,1)-summing, i.e. for…
Complex interpolation of spaces of operators on l_1
Andreas Defant, Carsten Michels
Within the theory of complex interpolation and theta-Hilbert spaces we extend classical results of Kwapien on absolutely (r,1)-summing operators on l_1 with values in l_p as well a…
Λ(p)-sets and the limit order of operator ideals
Carsten Michels
Given an infinite set Λof characters on a compact abelian group we show that Λis a Λ(p)-set for all p>2 if and only if the limit order of the ideal of all Λ-summing operators coinc…
A complex interpolation formula for tensor products of vector-valued Banach function spaces
Andreas Defant, Carsten Michels
We prove a complex interpolation formula for the injective tensor product of vector-valued Banach function spaces satisfying certain geometric assumptions. This result unifies resu…
Bennett-Carl inequalities for symmetric Banach sequence spaces and unitary ideals
Andreas Defant, Carsten Michels
We prove an abstract interpolation theorem which interpolates the (r,2)-summing and (s,2)-mixing norm of a fixed operator in the image and the range space. Combined with interpolat…