Print
Save
Email this link

Share Link

Copy this link, or click below to email it to a friend
Email this link
or copy the link directly:

https://akjournals.com/search?f_0=author&q_0=Sung+Guen+Kim
The link was not copied. Your current browser may not support copying via this button.

Link copied successfully

Search Results

You are looking at 1 - 2 of 2 items for

Author or Editor: Sung Guen Kim x

Refine by Access: All Content x

Clear All Modify Search

Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 54: Issue 3
DOI:: https://doi.org/10.1556/012.2017.54.3.1371

Author: Sung Guen Kim

We classify the extreme 2-homogeneous polynomials on $ℝ$ ² with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of $P (^{2} ℝ_{h (\frac{1}{2})}^{2})$ .

Restricted access

The unit balls of $ℒ (^{n} l_{\infty}^{m})$ and $ℒ_{s} (^{n} l_{\infty}^{m})$

Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 57: Issue 3
DOI:: https://doi.org/10.1556/012.2020.57.3.1470

Author: Sung Guen Kim

Abstract

For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

, where

ℒ ({}^{n}l_{\infty}^{m})

is the space of n-linear forms on

ℝ^{m}

with the supremum norm, and

ℒ_{s} ({}^{n}l_{\infty}^{m})

is the subspace of

ℒ ({}^{n}l_{\infty}^{m})

consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

, respectively. We show that ext

B_{ℒ ({}^{n}l_{\infty}^{m})}

⊂ ext

B_{ℒ ({}^{n}l_{\infty}^{m} + 1)}

, which answers the question in []. We show that every extreme point of the unit balls of

ℒ ({}^{n}l_{\infty}^{m})

and

ℒ_{s} ({}^{n}l_{\infty}^{m})

is exposed, correspondingly. We also show that

ext B_{ℒ_{s} ({}^{n}l_{\infty}^{2})} = ext B_{ℒ ({}^{n}l_{\infty}^{2})} \cap ℒ_{s} ({}^{n}l_{\infty}^{2}),

ext B_{ℒ_{s} ({}^{2}l_{\infty}^{m + 1})} \neq ext B_{ℒ ({}^{2}l_{\infty}^{m + 1})} \cap ℒ_{s} ({}^{2}l_{\infty}^{m + 1}),

exp B_{ℒ_{S} ({}^{n}l_{\infty}^{2})} = exp B_{ℒ ({}^{n}l_{\infty}^{2})} \cap ℒ_{s} ({}^{n}l_{\infty}^{2})

and $exp B_{ℒ_{s} ({}^{2}l_{\infty}^{m + 1})} \neq exp B_{ℒ ({}^{2}l_{\infty}^{m + 1})} \cap ℒ_{s} ({}^{2}l_{\infty}^{m + 1}),$

which answers the questions in [].

Restricted access

Browse Titles Subjects Subscriptions Frequently Asked Questions

For Authors Librarians About Us Journals

Our Blog Akademiai.hu Scientific Conferences Online Dictionary

Filter

Refine by Access

Refine by Collections

Refine by Type

Refine by Date

Share Link

Search Results

You are looking at 1 - 2 of 2 items for

Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants

The unit balls of $ℒ (^{n} l_{\infty}^{m})$ and $ℒ_{s} (^{n} l_{\infty}^{m})$

Abstract

Filter Filter

Refine by Access

Refine by Collections

Refine by Type

Refine by Date

Share Link

Search Results

You are looking at 1 - 2 of 2 items for

Extreme 2-homogeneous polynomials on the plane with a hexagonal norm and applications to the polarization and unconditional constants

The unit balls of ℒ ( n l ∞ m ) and ℒ s ( n l ∞ m )

Abstract

Filter

The unit balls of $ℒ (^{n} l_{\infty}^{m})$ and $ℒ_{s} (^{n} l_{\infty}^{m})$