Strong Proximinality and Renormings

نویسندگان

  • DARAPANENI NARAYANA
  • Jonathan M. Borwein
چکیده

We characterize finite-dimensional normed linear spaces as strongly proximinal subspaces in all their superspaces. A connection between upper Hausdorff semi-continuity of metric projection and finite dimensionality of subspace is given.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Proximinality properties in Lp (μ,X) and polyhedral direct sums of Banach spaces

For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. Let (P) be either proximinality or strong 1 1 2 -ball property and if (P) is separably determined for Y in X, then we prove that L1(μ, Y ) has the same property (P) in L1(μ,X). For an M -embedded space X, we give a class of elements in L1(μ,X ∗∗) having best approximations from L1(μ,X). We also pr...

متن کامل

Strong proximinality and intersection properties of balls in Banach spaces

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z ⊆ Y ⊆ X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M -ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proxi...

متن کامل

On the Proximinality of Ridge Functions

Using two results of Garkavi, Medvedev and Khavinson [7], we give sufficient conditions for proximinality of sums of two ridge functions with bounded and continuous summands in the spaces of bounded and continuous multivariate functions respectively. In the first case, we give an example which shows that the corresponding sufficient condition cannot be made weaker for some subsets of Rn. In the...

متن کامل

Remotality and proximinality in normed linear spaces

In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.

متن کامل

Transitivity of various notions of proximinality in Banach spaces

We derive transitivity of various degrees of proximinality in Banach spaces. When the transitivity does not carry forward to the bigger space we investigate these properties under some additional assumptions of the intermediate space. For instance, we show that if Z ⊆ Y ⊆ X where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X then Z is stro...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005