Related papers: A remark on continuity of positive linear function…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

We study Bohr's theorem for vector valued holomorphic and operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using invariants from local Banach space theory, we show that the associated Bohr radius is…

Let $X$ and $Y$ be Banach or normed linear spaces and $F\subset X$ a closed set. We apply our recent extension theorem for vector-valued Baire one functions arXiv:1512.03717 to obtain an extension theorem for vector-valued functions…

We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let $Mod(\tau)$ be the set of countable structures with universe $\omega$ in vocabulary $\tau$ topologized by the Scott topology. We show that an invariant…

Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, a functional limit…

Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps in a metric space are…

For a locally compact Hausdorff space $L$, we denote by $C_0(L,\mathbb{R})$ the Banach space of all continuous real-valued functions on $L$ vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry…

Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgroup of G is separable. This is proven for G=SL_n(Z).…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…

In a previous paper the second author introduced a compact topology on the space of closed ideals of a unital Banach algebra A. If A is separable then this topology is either metrizable or else neither Hausdorff nor first countable. Here it…

We show that if the Kobayashi--Royden metric of a complex manifold is continuous and positive at a given point and any non-zero tangent vector, then the "derivatives" of the higher order Lempert functions exist and equal the respective…

We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homomorphism thus generalising Aupetit's 1998 result for finite…

Let $\mathfrak{J}$ be a JB$^*$-algebra with no quotients isomorphic to $S_2(\mathbb{C})$. Let $\mu$ be a local quasi-linear Jordan functional on $\mathfrak{J}_{sa}$. We show that $\mu$ is a linear functional on $\mathfrak{J}_{sa}$ if and…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

In this work, we extend the theory of B\'ekoll\`e-Bonami $B_p$ weights. Here we replace the constant $p$ by a non-negative measurable function $p(\cdot),$ which is log-H\"older continuous function with lower bound $1$. We show that the…

For a metric compact space $L$ and a Banach space $E$, we provide a characterization of the complementability of the Banach space $\mathcal{C}(L)$ of continuous functions on $L$ inside $E$ in terms of the existence of a certain tree in the…

We generalize to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szeg\"o $L^p$-distance estimate, and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. In so doing, we…

We study strongly separately continuous real-valued function defined on the Banach spaces $\ell_p$. Determining sets for the class of strongly separately continuous functions on $\ell_p$ are characterized. We prove that for every $1\le…

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff…