1. Projecting the space of bonded operators onto the space of compact operators
- Author
-
A. Tong
- Subjects
Sequence ,Pure mathematics ,Applied Mathematics ,General Mathematics ,Bounded function ,Linear operators ,Topological space ,Compact operator ,Space (mathematics) ,Subspace topology ,Compact operator on Hilbert space ,Mathematics - Abstract
This paper studies the existence of bounded projections from the space B(X, Y) of bounded linear operators onto the subspace K(X, Y) of compact linear operators, where X and Y are normed spaces. For the cases where X and Y are either the I, or co spaces, the problem was first answered by E. Thorp [3 ]. For the cases where X is an infinite dimensional L-space or where Y is the space of all continuous functions on a topological space, various theorems were given by Arterburn and Whitley [1]. Owing to a recent result in [4], we will show that a more decisive answer can be given for the case where X, Y are Banach sequence spaces when the problem is considered from the approach of Thorp [3]. (See (1.2), (2.1), and (2.4).)
- Published
- 1970