On Weak Operator Compactness of the Unit Ball ofL(H)

1978 ◽  
Vol 24 (31-36) ◽  
pp. 493-494 ◽  
Author(s):  
Douglas S. Bridges
Keyword(s):  
Unit Ball ◽  
Weak Operator

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

scholarly journals Homogeneously Polyanalytic Kernels on the Unit Ball and the Siegel Domain

2021 ◽  
Vol 15 (6) ◽  
Author(s):  
Christian Rene Leal-Pacheco ◽  
Egor A. Maximenko ◽  
Gerardo Ramos-Vazquez
Keyword(s):  
Unit Ball ◽  
Siegel Domain

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

scholarly journals EPTAS and Subexponential Algorithm for Maximum Clique on Disk and Unit Ball Graphs

2021 ◽  
Vol 68 (2) ◽  
pp. 1-38
Author(s):  
Marthe Bonamy ◽  
Édouard Bonnet ◽  
Nicolas Bousquet ◽  
Pierre Charbit ◽  
Panos Giannopoulos ◽  
...  
Keyword(s):  
Unit Ball ◽  
Maximum Clique ◽  
Subexponential Algorithm

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

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