BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space

2010 ◽  
Vol 348 (21-22) ◽  
pp. 1175-1178
Author(s):  
Michael Röckner ◽  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
Hilbert Space ◽  
Convex Set ◽  
Bv Functions ◽  
Gelfand Triple

scholarly journals The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

2012 ◽  
Vol 40 (4) ◽  
pp. 1759-1794 ◽  
Author(s):  
Michael Röckner ◽  
Rong-Chan Zhu ◽  
Xiang-Chan Zhu
Keyword(s):  
Convex Set ◽  
Infinite Dimensional ◽  
Bv Functions ◽  
Gelfand Triple

scholarly journals SPECTRUM, NUMERICAL RANGE AND DAVIS-WIELANDT SHELL OF A NORMAL OPERATOR

2009 ◽  
Vol 51 (1) ◽  
pp. 91-100 ◽  
Author(s):  
CHI-KWONG LI ◽  
YIU-TUNG POON
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Numerical Range ◽  
Normal Operator ◽  
Additional Information ◽  
Commuting Operators ◽  
Boundary Points ◽  
Reducing Subspace ◽  
Joint Numerical Range

AbstractWe denote the numerical range of the normal operator T by W(T). A characterization is given to the points in W(T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W(T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, such a boundary point always associates with an invariant (reducing) subspace of the normal operator. It follows that a normal operator acting on a separable Hilbert space cannot have a closed strictly convex set as its numerical range. Similar results are obtained for the Davis-Wielandt shell of a normal operator. One can deduce additional information of the normal operator by studying the boundary of its Davis-Wielandt shell. Further extension of the result to the joint numerical range of commuting operators is discussed.

Extreme Points of the Convex set of Stochastic Maps on A C*-Algebra

1998 ◽  
Vol 01 (04) ◽  
pp. 599-609 ◽  
Author(s):  
K. R. Parthasarathy
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Convex Set ◽  
Convex Combination ◽  
Extreme Points ◽  
Bounded Operators ◽  
Completely Positive ◽  
C Algebra ◽  
Permutation Matrices ◽  
Normal Maps

Let [Formula: see text] be a unital C*-subalgebra of the C*-algebra ℬ(ℋ) of all bounded operators on a complex separable Hilbert space ℋ. Let [Formula: see text] denote the convex set of all unital, linear, completely positive and normal maps of [Formula: see text] into itself. Using Stinespring's theorem, we present a criterion for an element [Formula: see text] to be extremal. When [Formula: see text], this criterion leads to an explicit description of the set of all extreme points of [Formula: see text]. We also obtain a quantum probabilistic analogue of the classical Birkhoff's theorem2 that every bistochastic matrix can be expressed as a convex combination of permutation matrices.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

scholarly journals BV functions in a Gelfand triple for differentiable measure and its applications

2015 ◽  
Vol 27 (3) ◽  
Author(s):  
Michael Röckner ◽  
Rongchan Zhu ◽  
Xiangchan Zhu
Keyword(s):  
Dirichlet Form ◽  
Adjoint Operator ◽  
Stochastic Quantization ◽  
Bv Functions ◽  
Form Theory ◽  
Differentiable Measure ◽  
Definition Of ◽  
Non Gaussian ◽  
Gelfand Triple ◽  
Quantization Problem

AbstractIn this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759–1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator

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