Proximinality in Subspaces of c0
نویسندگان
چکیده
منابع مشابه
PFA and complemented subspaces of ℓ∞/c0
The Banach space `∞/c0 is isomorphic to the linear space of continuous functions on N∗ with the supremum norm, C(N∗). Similarly, the canonical representation of the `∞ sum of `∞/c0 is the Banach space of continuous functions on the closure of any non-compact cozero subset of N∗. It is important to determine if there is a continuous linear lifting of this Banach space to a complemented subset of...
متن کاملOn the Proximinality of the Unit Ball of Proximinal Subspaces in Banach Spaces: a Counterexample
A known, and easy to establish, fact in Best Approximation Theory is that, if the unit ball of a subspace G of a Banach space X is proximinal in X, then G itself is proximinal in X. We are concerned in this article with the reverse implication, as the knowledge of whether the unit ball is proximinal or not is useful in obtaining information about other problems. We show, by constructing a count...
متن کاملProximinality and co-proximinality in metric linear spaces
As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces. A new kind of ...
متن کاملON SUBSPACES OF c0 AND EXTENSION OF OPERATORS INTO C(K )-SPACES
Johnson and Zippin recently showed that if X is a weak∗-closed subspace of 1 and T : X → C(K ) is any bounded operator then T can be extended to a bounded operator T̃ : 1 → C(K ). We give a converse result: if X is a subspace of 1 such that 1/X has an unconditional finitedimensional decomposition (UFDD) and every operator T : X → C(K ) can be extended to 1 then there is an automorphism τ of 1 su...
متن کاملStability of ball proximinality
In this paper, we show that if E is an order continuous Köthe function space and Y is a separable subspace ofX, then E(Y ) is ball proximinal in E(X) if and only if Y is ball proximinal in X. As a consequence, E(Y ) is proximinal in E(X) if and only if Y is proximinal in X. This solves an open problem of Bandyopadhyay, Lin and Rao. It is also shown that if E is a Banach lattice with a 1-uncondi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1999
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3382