Events of Functional Analysts

 at NSYSU, 2016



Department of Applied Mathematics


National Sun Yat-sen University, Kaohsiung, Taiwan.

台灣•高雄•中山大學•應用數學系


 

Several functional analysts are visiting National Sun Yat-sen University and offering workshops below.  All interested are welcome to join.

 

I.     Mini-workshop in Functional Analysis, Day 1,

Thursday, May 19, 2016. Venue: SC-4013, NSYSU

 

1.    L. Molnár (University of Szeged, Hungary): Transformations on positive matrices and operators (13:10-13:55pm)

We survey results concerning different sorts of transformations on the cones of positive semidefinite or positive definite matrices and operators. The transformations in question are maps preserving certain important operations, or distances (or even so-called generalized distance measures), or partial orders. Hence, they are kinds of isomorphisms, or "generalized" isometries. In the talk we shall describe their precise structures.

 

2.    D. Virosztek (Budapest University of Technology and Economics, Hungary): Continuous Jordan triple endomorphisms of   (14:00-14:45pm)

We describe the structure of all continuous Jordan triple endomorphisms of the set  of all positive definite 2x2 matrices. We also mention an application concerning sorts of surjective generalized isometries on  and, as second  application, we complete a former result on the structure of sequential endomorphisms of finite dimensional effect algebras. Furthermore, we characterize the continuous endomorphisms of the space of three-dimensional velocity vectors with respect to the Einstein addition (or relativistic sum). Joint work with Lajos Molnár.

 

3.    Gy. P. Gehér (University of Szeged, Hungary): Is it possible to determine a point lying in a simplex if we know the distances from the vertices? (15:00-15:45pm)

It is an elementary fact that if we fix an arbitrary set of  affine independent points  in , then the Euclidean distances  determine the point  in  (and therefore in the simplex ) uniquely.  In my talk I would like to investigate a similar problem in general normed spaces.  Npmely, I will present a characterization of those, at least -dimensional, real normed spaces  for which every set of  affine independent points , the distances  determine the point  lying in the simplex  uniquely. Surprisingly, the characterization depends on .

 

4.    Hongke Du 杜鴻科 (Shannxi Normal University, China): Uniteries of Krein space  (15:55-16:40pm)

In this talk, we will discuss the block-operator expression and connectivity of Uniteries in Krein space .

 

5.    Denny Leung 梁浩瀚(National University of Singapore): Inverses of disjointness preserving operators (16:50-17:35pm)

A linear operator between (possibly vector-valued) function spaces is disjointness preserving if it maps disjoint functions to disjoint functions.  Here, two functions are said to be disjoint if at least one of them vanishes at each point.  Linear disjointness preserving operators have been well studied.  A particular question of interest is when the inverse of a disjointness preserving linear isomorphism must also be disjointness preserving.  In this talk, we consider this question for operators on various types of function spaces, including spaces of (little) Lipschitz functions, uniformly continuous functions and differentiable functions.  It is shown that a disjointness preserving linear isomorphism whose domain is one of these types of spaces (scalar-valued) has a disjointness preserving inverse, subject to some topological conditions on the range space.  A representation for a general linear disjointness preserving operator on a space of vector-valued  functions is also given.

 

This talk is based on joint work with Li Lei (Nankai U) and Wang Ya-shu (National Chung Hsing U).

 

II.  Mini-workshop in Functional Analysis, Day 2,

Tuesday, May 24, 2016. Venue: SC-4011, NSYSU

 

6.    Hao-Wei Huang (NSYSU, Taiwan): Analytic and combinatorial aspects of bi-freely infinitely divisible laws (14:10-14:55pm)

In free probability the notion of free convolution of probability distributions on  has played an important role since its inception by D. Voiculescu some 30 years ago. In 2013, Voiculescu generalized the notion of free independence to study left and right actions on reduced free product spaces simultaneously, known as bi-free independence. One generalization of the free convolution to the bi-free setting is the bi-free convolution of planar probability distributions. In this talk, we will explain that the bi-freely infinitely divisible laws, and only these laws, can be used to approximate the distributions of sums of identically distributed bi-free pairs of commuting faces. We will also talk about bi-free Levy-Khintchine representations from an infinitesimal point of view. The proofs depend on the bi-free harmonic analysis machinery that we developed for integral transforms of two variables, and the combinatorics of moments and bi-free cumulants. If time permits, some recent developments in this direction will also be discussed.

 

7.    D. Virosztek (Budapest University of Technology and Economics, Hungary): Maps on quantum states and positive definite matrices preserving Bregman and Jensen divergences (15:00-15:45pm)

We describe the structure of all bijective maps on the state space of a finite quantum system which preserve Bregman or Jensen divergences. Similar results concerning the cone of positive definite matrices are also given. We would like to highlight how essentially different techniques lead to the description of the generalized isometries in the two aforementioned cases. Partially based on a joint work with Lajos Molnár and József Pitrik.

 

8.    Gy. P. Gehér (University of Szeged, Hungary): Isometries of Grassmann spaces (16:00-16:45pm)

Botelho,  Jamison,  and  Molnár  have  recently  described  the  general  form  of  surjective  isometries  of  Grassmann  spaces on complex Hilbert spaces under certain dimensionality assumptions. In this talk we provide a new approach to this problem which enables us first, to give a shorter proof and second, to remove dimensionality constraints completely. In one of the low dimensional cases, which was not covered by Botelho, Jpmison,  and Molnár, an exceptional possibility occurs. As a byproduct, we are able to handle the real case as well. Furthermore, in finite dimensions we remove the surjectivity assumption. A variety of tools is used in order to achieve our goal.

 

9.    Hongke Du杜鴻科(Shannxi Normal University, China): Block-operator expression and connectivity of Lagrangian Grassmannian  (16:50-17:35pm)

In this talk, we will use the block-operator technique and spectral theory of operators to study  the expression and connectivity of Lagrangian Grassmannian .

 

Sponsors:  National Center of Theoretical Sciences (Math, Taipei), Ministry of Science and Technology, and National Sun Yat-sen University.

 

Contact:    

Ngai-Ching Wong黃毅青, wong@math.nsysu.edu.tw, Tel: (886) 7-525-2000 ext. 3818,

Chia-Feng Yen 嚴嘉鳳, yencf@math.nsysu.edu.tw, Tel: (886) 7-5252000 ext. 3849; or visit

 


http://www.math.nsysu.edu.tw/~wong/FA2016