Related papers: On isometric reflexions in Banach spaces

We carry out a systematic study of decidability for theories of (a) real vector spaces, inner product spaces, and Hilbert spaces and (b) normed spaces, Banach spaces and metric spaces, all formalised using a 2-sorted first-order language.…

We show that there exists a Banach space $E$ with the following properties: the Banach algebra $\mathscr{B}(E)$ of bounded, linear operators on $E$ has a singular extension which splits algebraically, but it does not split strongly, and the…

An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove…

The irreducible unitary representations of the Banach Lie group $U_0(\H)$ (which is the norm-closure of the inductive limit $\cup_k U(k)$) of unitary operators on a separable Hilbert space $\H$, which were found by Kirillov and Ol'shanskii,…

Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D \mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge…

We refine the well-known Blanco-Koldobsky-Turn\v{s}ek Theorem which states that a norm one linear operator defined on a Banach space is an isometry if and only if it preserves orthogonality at every element of the space. We improve the…

In this paper we investigate real convex-transitive Banach spaces X, which admit a 1-dimensional bicontractive projection P on X. Various mild conditions regarding the weak topology and the geometry of the norm are provided, which guarantee…

In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of…

We prove several results asserting that the action of a Banach-Lie group on Hilbert spaces of holomorphic sections of a holomorphic Hilbert space bundle over a complex Banach manifold is multiplicity free. These results require the…

If $Q$ is a surjection from $L^1(\mu)$, $\mu$ $\sigma$-finite, onto a Banach space containing $c_0$ then (*) $\ker Q$ is uncomplemented in its second dual. If $Q$ is a surjection from an ${\cal L}_1$-space onto a Banach space containing…

A bounded operator on a real or complex separable infinite-dimensional Banach space $Z$ is universal in the sense of Glasner and Weiss if for every invertible ergodic measure-preserving transformation $T$ of a standard Lebesgue probability…

Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.

In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular…

If $X$ is a compact Hausdorff space and $\sigma$ is a homeomorphism of $X$, then a Banach algebra $\ell^1(\Sigma)$ of crossed product type is naturally associated with this topological dynamical system $\Sigma=(X,\sigma)$. If $X$ consists…

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not…

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex…

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…

Let $S$ be a closed subset of a Banach space $X$. Assuming that $S$ is epi-Lipschitzian at $\bar{x}$ in the boundary $ \bd S$ of $S$, we show that $S$ is strictly Hadamard differentiable at $\bar{x}$ IFF the Clarke tangent cone $T(S,…

A set of all symmetric Banach function spaces defined on [0,1] is equipped with the partial order by the relation of continuous inclusion. Properties of symmetric spaces, which do not depend of their position in the ordered structure, are…

Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…