On quasi-denting points, denting faces and the geometry of the unit ball ofd(w, 1)

1994 ◽  
Vol 63 (1) ◽  
pp. 45-55 ◽  
Author(s):  
A. Molt� ◽  
V. Montesinos ◽  
S. Troyanski
Keyword(s):  
Unit Ball ◽  
Denting Points

scholarly journals There are no denting points in the unit ball of 𝒫(2H)

2002 ◽  
Vol 66 (3) ◽  
pp. 497-498
Author(s):  
Sung Guen Kim
Keyword(s):  
Hilbert Space ◽  
Unit Ball ◽  
Real Hilbert Space ◽  
Homogeneous Polynomials ◽  
Infinite Dimensional ◽  
Strongly Exposed Points ◽  
Denting Points

For any infinite dimensional real Hilbert space H we show that the unit ball of the space of continuous 2-homogeneous polynomials on H, 𝒫(2H), has no denting points. Thus the unit ball of 𝒫(2H) has no strongly exposed points.

Strict U-Ideals and U-Summands in Banach Spaces

2014 ◽  
Vol 114 (2) ◽  
pp. 216 ◽  
Author(s):  
Trond A. Abrahamsen
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Extension Operator ◽  
Denting Points ◽  
Set Of Points

For a strict u-ideal $X$ in a Banach space $Y$ we show that the set of points in the dual unit ball $B_{X^{\ast}}$, strongly exposed by points in the range $\it TY$ of the unconditional extension operator $T$ from $Y$ into the bidual $X^{\ast\ast}$ of $X$, is contained in the weak$^{\ast}$ denting points in $B_{X^{\ast}}$. We also prove that a u-embedded space is a u-summand if and only if it contains no copy of $c_0$ if and only if it is weakly sequentially complete.

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.

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