Annali di Matematica https://doi.org/10.1007/s10231-018-0760-x Centralizers on a super-reﬂexive Schatten ideal Jesús Suárez de la Fuente Received: 8 January 2018 / Accepted: 12 May 2018 © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We give a simple proof that there is no strictly singular bicentralizer on a super- reﬂexive Schatten ideal. This result applies, in particular, to the p-Schatten class for 1 < p < ∞. Keywords Schatten · Strictly singular · Bicentralizer Mathematics Subject Classiﬁcation Primary: 46A16 · 46B07 · 46B20 1Main Let H be a separable Hilbert space and denote by B(H ) the algebra of all bounded linear operators on H . We will follow the deep work of Kalton , the interested reader may consider also [2,3], to introduce the following deﬁnitions. Let E be a Köthe sequence space which is symmetric, then we deﬁne the corresponding Schatten ideal C to be the algebra of all operators A : H → H whose singular values s (A) satisfy that (s (A)) ∈ E.We n n endow C with the norm A =(s (A)) . In this notation, the usual p-Schatten class E E n E is
Annali di Matematica Pura ed Applicata (1923 -) – Springer Journals
Published: May 29, 2018
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