Anti-derivable linear maps at zero on standard operator algebras

Acta Mathematica Hungarica - Let $$\mathcal{X}$$ be a complex Banach space with $$\dim \mathcal{X}\geq 2$$ , and $$\mathcal{A} \subseteq \mathcal{B}(\mathcal{X})$$ be a standard operator algebra....     

Maps preserving a certain product of operators

Let $$\mathcal {A}$$ be a standard operator algebra on a Banach space $$\mathcal {X}$$ with $$ \dim \mathcal {X}\ge 3$$. In this paper, we determine the form of the bijective maps $$\phi :\mathcal {A}\longrightarrow \mathcal {A}$$ satisfying $$\begin{aligned} \phi \left( \frac{1}{2}(AB^2+B^2A)\right) = \frac{1}{2}[\phi (A)\phi (B)^{2}+\phi (B)^{2}\phi (A)], \end{aligned}$$for every $$A,B \in \mathcal {A}$$.     

Weak law of large numbers for iterates of random-valued functions

Aequationes mathematicae - Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ , a complete and separable metric space X with the $$ \sigma $$ -algebra $$ {\mathcal {B}} $$ of all its...     

A note on strong skew Jordan product preserving maps on von Neumann algebras

Periodica Mathematica Hungarica - Let $$\mathcal {A}$$ be a von Neumann algebra acting on the complex Hilbert space $$\mathcal {H}$$ and $$\Phi {:}\,\mathcal {A} \longrightarrow \mathcal {A}$$ be a...     

Reduced Minimum Modulus Preserving in Banach Space

Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].      

The Monge Problem in Banach Spaces

In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function . A K?the functional is defined by (P, Q) = inf where is the law of X. If c is a profit function, we note . (P, Q) = sup Under some conditions, we show the existence of a Monge function, φ, such that , or .      

Spectral Shorted Operators

If $$\mathcal{H}$$ is a Hilbert space, $$\mathcal{S}$$ is a closed subspace of $$\mathcal{H},$$ and A is a positive bounded linear operator on $$\mathcal{H},$$ the spectral shorted operator $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence $$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes $$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to $$\mathcal{S}.$$ We characterize the left spectral resolution of $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ and show several properties of this operator, particularly in the case that dim $${\mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional case and for non invertible operators.     

Generation in singularity categories of hypersurfaces of countable representation type

The Orlov spectrum and Rouquier dimension are invariants of a triangulated category to measure how big the category is, and they have been studied actively. In this paper, we investigate the singularity category $$\textsf {D} _{\textsf {sg} }(R)$$ of a hypersurface R of countable representation type. For a thick subcategory $${\mathcal {T}}$$ of $$\textsf {D} _{\textsf {sg} }(R)$$ and a full subcategory $$\mathcal {X}$$ of $${\mathcal {T}}$$, we calculate the Rouquier dimension of $${\mathcal {T}}$$ with respect to $$\mathcal {X}$$. Furthermore, we prove that the level in $$\textsf {D} _{\textsf {sg} }(R)$$ of the residue field of R with respect to each nonzero object is at most one.     

The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle

Geometriae Dedicata - Let $$\pi :\mathcal {X}\rightarrow M$$ be a holomorphic fibration with compact fibers and L a relatively ample line bundle over $$\mathcal {X}$$ . We obtain the asymptotic of...     

The primitive spectrum of a semigroup of Markov operators

Positivity - For a semigroup $$\mathcal {S}$$ of Markov operators on a space of continuous functions, we use $$\mathcal {S}$$-invariant ideals to describe qualitative properties of $$\mathcal {S}$$...     

Paranormal measurable operators affiliated with a semifinite von Neumann algebra. II

Positivity - Let $${{\mathcal {M}}}$$ be a von Neumann algebra of operators on a Hilbert space $${\mathcal {H}}$$ and $$\tau $$ be a faithful normal semifinite trace on $$\mathcal {M}$$ . Let...     

On $$A_1^2$$ A 1 2 restrictions of Weyl arrangements

Journal of Algebraic Combinatorics - Let $$\mathcal {A}$$ be a Weyl arrangement in an $$\ell $$ -dimensional Euclidean space. The freeness of restrictions of $$\mathcal {A}$$ was first settled by a...     

Resolvent norm decay does not characterize norm continuity

We show that there exists a reflexive Banach space $ (\mathcal{X},\parallel .\parallel ) We show that there exists a reflexive Banach space and a strongly continuous semigroup with generator on such that but is not eventually norm continuous. This answers a question of Amnon Pazy in the negative. This research was carried out during the author’s stay at Arbeitsgruppe Funktionalanalysis of Universit?t Karlsruhe with the support of the Alexander von Humboldt-Stiftung and of the Gemeinnützige Hertie-Stiftung. The research was partially supported by the OTKA Grants F 43620, T 49786 and T 37758.     

Über die Starrheit kompakter komplexer Räume

This article deals with deformations of compact complex spaces, the parameter-space being a general complex space. A compact space X₀ is called absolutely rigid, if every deformation of X₀ is trivial. Ex(X₀, ) is defined as the group of the extensions of by and it is shown that X₀ is absolutely rigid if and only if Ex(X₀, )=0.If X₀ is reduced, there is Ex(X₀, ). The proof makes use of the results of M.A{uprtin} [1] and D{upouady} [2].     

Stable Phase Retrieval in Infinite Dimensions

Foundations of Computational Mathematics - The problem of phase retrieval is to determine a signal $$f\in \mathcal {H}$$ , with $$ \mathcal {H}$$ a Hilbert space, from intensity measurements...     

Endpoint Estimates for the Maximal Function over Prime Numbers

Journal of Fourier Analysis and Applications - Given an ergodic dynamical system $$(X, \mathcal {B}, \mu , T)$$, we prove that for each function f belonging to the Orlicz space $$L(\log L)^2(\log...     

Continuity of $$L_{p}$$ Balls and an Application to Input-Output Systems

Mathematical Notes - In this paper, the continuity of the set-valued map $$p\rightarrow B_{\Omega,\mathcal{X},p}(r)$$ , $$p\in (1,+\infty)$$ , is proved where $$B_{\Omega,\mathcal{X},p}(r)$$ is the...     

The Topology on the Space of δ-psh Functions in the Cegrell Classes

The aim of the present paper is to introduce a metric locally convex topology on the space of δ-psh functions in the Cegrell class . We prove that with this topology is a non-separable and non-reflexive Fréchet space. At the same time, we extend the Monge–Ampère operator from the class to .     

Topological Factors Derived from Bohmian Mechanics

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space $$ \mathcal{Q}. $$ These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of $$ \mathcal{Q}. $$ We employ wave functions on the universal covering space of $$ \mathcal{Q}. $$ As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric. Communicated by Yosi Avron Submitted: 21/06/2005 Revised: 10/01/2006 Accepted: 27/01/2006     

On the best bound of the minimal twisted height of linear subspaces

Let V be a vector space over a global field k, g an element of the adele group and H_g the twisted height defined on the k-subspaces of V . We show that the square root of the generalized Hermite-Rankin constant for k gives the best upper bound of the function , where runs over all m-dimensional k-subspaces of V and runs over all n-dimensional k-subspaces of . Received: 17 June 2005