S. Troyanski

activity

20152020

collaborators

Showing math.FAShow all

6 papers · 1 filter

math.FA2020

Daugavet- and delta-points in Banach spaces with unconditional bases

Trond A. Abrahamsen, Vegard Lima, André Martiny +1

We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a $1$ -unconditional basis. A norm one element $x$ in a Banach space is a Daugavet-poin…

math.FA2020

Spaces C(K) with an equivalent URED norm

Antonio Avilés, Stanimir Troyanski

We prove that a Banach space of continuous functions $C (K)$ has a renorming that is uniformly rotund in every direction (URED) if and only if the compact space $K$ supports a stric…

math.FA2019

Almost square dual Banach spaces

Trond A. Abrahamsen, Petr Hájek, Stanimir Troyanski

We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on $ℓ_{\infty} .$ As a…

math.FA2018

Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts

S. P. Gul'ko, A. V. Ivanov, M. S. Shulikina +1

We show that $C (X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ adm…

math.FA2018

Norming subspaces of Banach spaces

Vladimir P. Fonf, Sebastian Lajara, Stanimir Troyanski +1

We show that, if $X$ is a closed subspace of a Banach space $E$ and $Z$ is a closed subspace of $E^{*}$ such that $Z$ is norming for $X$ and $X$ is total over $Z$ (as well as $X$ is…

math.FA2015

Diameter 2 properties and convexity

Trond A. Abrahamsen, Peter Hájek, Olav Nygaard +2

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C [0, 1]$ on which every weakly compact projection $P$ satisfies the equation $∥ I - P ∥ = 1 + ∥ P ∥$ …