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7 papers · 1 filter
A version of Lomonosov's theorem for collections of positive operators
Alexey I. Popov, Vladimir G. Troitsky
It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zer…
Majorizing measures and proportional subsets of bounded orthonormal systems
Olivier Guedon, Shahar Mendelson, Alain Pajor +1
In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in , and any , there exists a subset of cardinali…
The amenability constant of the Fourier algebra
Volker Runde
For a locally compact group , let denote its Fourier algebra and its dual object, i.e. the collection of equivalence classes of unitary represenations of . W…
On convexified packing and entropy duality
S. Artstein, V. Milman, S. J. Szarek +1
A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sen…
A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal
Volker Runde
Let be a locally compact group, and let denote the space of weakly almost periodic functions on . We show that, if is a -group, but not compact, then the…
Minimal vectors in arbitrary Banach spaces
Vladimir G. Troitsky
We extend the method of minimal vectors to arbitrary Banach spaces. It is proved, by a variant of the method, that certain quasinilpotent operators on arbitrary Banach spaces have…