arXiv subjects

E. M. Semenov

Publications and source records attributed to E. M. Semenov.

2 recordsLinked to original sources

arXiv2010

Kruglov operator and operators defined by random permutations

The Kruglov property and the Kruglov operator play an important role in the study of geometric properties of r.i. function spaces. We prove that the boundedness of the Kruglov operator in a r.i. space is equivalent to the uniform boundedness on this space of a sequence of operators defined by random permutations. It is shown also that there is no minimal r.i. space with the Kruglov property.

math.FA↗

arXiv2000

Embeddings of rearrangement invariant spaces that are not strictly singular

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L_1([0,1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L_Phi with Phi(x) = exp(x^2)-1.

math.FA↗