Related papers: Operator space complexification transfigured

In this work we study the following three space problem for operator spaces: if X is an operator space with base space isomorphic to a Hilbert space and X contains a completely isomorphic copy of the operator Hilbert space OH with…

Let $H$ be a separable complex Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian consisting of closed linear subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion…

If $X$ is a connected complex manifold with $d_X = 2$ that admits the holomorphic and transitive action of a (connected) Lie group $G$, then the action extends to an action of the complexification $\hat{G}$ of $G$ on $X$ except when either…

Let X be an irreducible reduced complex space on which a connected compact Lie group K acts by holomorphic automorphisms. Let G be the complexification of K and g the Lie algebra of G. Following the theory of algebraic transformation…

Let X be a proper metric space, which has finite asymptotic dimension in the sense of Gromov (or more generally, straight finite decomposition complexity of Dranishnikov and Zarichnyi). New descriptions are provided of the Roe algebra of X:…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…

A consistent description of images on the disk and of their transformations is given as elements of a vector space and of an operators algebra. The vector space of images on the disk $\mathbb{D}$ is the Hilbert space $L^2(\mathbb{D})$ that…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

Let X=G/K be a connected Riemannian homogeneous space of a real Lie group G. The homogeneous space X is called commutative if the algebra of G-invariant differential operators on X is commutative. We prove an effective commutativity…

This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.

Given a topological group $G$ and a unitary representation $U$ of $G$, we consider the problem of classifying the positive operator measures which are based on a $G$-homogeneous space $X$ and covariant with respect to the representation…

For a separable complex Hilbert space $H$, we say that a bounded linear operator $T$ acting on $H$ is $C$-normal, where $C$ is a conjugation on $H$, if it satisfies $CT^*TC=TT^*$. For a normal operator, we give geometric conditions which…

Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially…

A large literature specifies conditions under which the information complexity for a sequence of numerical problems defined for dimensions $1, 2, \ldots$ grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus…

Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $\sH$ with a multivalued part $\mul A$. An operator $B$ in $\sH$ with $\ran B\perp\mul A^{**}$ is said to be an operator part of $A$ when $A=B \hplus (\{0\}\times \mul…

If $g$ is an analytic function in the unit disc $\D $ we consider the generalized Hilbert operator $\hg$ defined by {equation*}\label{H-g} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt. {equation*} We study these operators acting on classical…