Related papers: Noncommutative Valdivia compacta

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every…

We study classes of Banach spaces where the points of weak$^*$-weak continuity for the identity mapping on the dual unit ball form a weak$^*$-dense and weak$^*$-$G_{\delta}$ set. We also discuss how this property behaves in higher duals of…

Let $T:X\to X$ be a linear power bounded operator on Banach space. Let $X_0$ is a subspace of vectors tending to zero under iterating of $T$. We prove that if $X_0$ is not equal to $X$ then there exists $\lambda$ in Sp(T) such that, for…

Motivated by the question of Mikael de la Salle, we investigate the problem of the existence of equivalent strictly convex norms on Banach spaces that are invariant with respect to an action of a group by linear isometries. We develop…

In the present paper, the following convexity principle is proved: any closed convex multifunction, which is metrically regular in a certain uniform sense near a given point, carries small balls centered at that point to convex sets, even…

We construct a ZFC example of a nonmetrizable compact space $K$ such that every totally disconnected closed subspace $L\subseteq K$ is metrizable. In fact, the construction can be arranged so that every nonmetrizable compact subspace may be…

We provide a ZFC example of a compact space K such that C(K)* is w*-separable but its closed unit ball is not w*-separable. All previous examples of such kind had been constructed under CH. We also discuss the measurability of the supremum…

The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…

We develop a $d$-variable analog of the two-component de Bran-ges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in…

We show that it is consistent that for some uncountable cardinal k, all compactifications of the countable discrete space with remainders homeomorphic to $D^k$ are homeomorphic to each other. On the other hand, there are $2^c$ pairwise…

We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak…

In this article we study commutant lifting, more generally intertwining lifting, for different reproducing kernel Hilbert spaces over two domains in $\mathbb{C}^n$, namely the unit ball and the unit polydisc. The reproducing kernel Hilbert…

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is…

We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its…

In the present paper we prove that a necessary condition for a Banach space $X$ to admit a generating compact Lipschitz retract $K$, which satisfies an additional mild assumption on its shape, is that $X$ enjoys the Bounded Approximation…

We construct a totally disconnected compact Hausdorff space N which has clopen subsets M included in L included in N such that N is homeomorphic to M and hence C(N) is isometric as a Banach space to C(M) but C(N) is not isomorphic to C(L).…

Suppose that $Q$ is a weak$^{\ast }$ compact convex subset of a dual Banach space with the Radon-Nikod\'{y}m property. We show that if $(S,Q)$ is a nonexpansive and norm-distal dynamical system, then there is a fixed point of $S$ in $Q$ and…

We prove that if $ C $ is a family of separable Banach spaces which is analytic with respect to the Effros-Borel structure and none member of $ C $ is isometrically universal for all separable Banach spaces, then there exists a separable…

Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace…

Given a Banach space. We show that its three times dual space can be written as a direct sum. Then being one of the sumands null is a necessary and sufficient condition for the dual space to be reflexive. We end with an application of this…