Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Complemented Subspaces of Linear Bounded Operators

 Read article[PDF: 204KB]
Published:2011-05-20
Printed: Sep 2012
• Manijeh Bahreini,
University of Isfahan, Department of Mathematics, Isfahan 81745-163, Iran
• Elizabeth Bator,
University of North Texas, Department of Mathematics, Denton, Texas 76203-1430
• Ioana Ghenciu,
University of Wisconsin-River Falls, Department of Mathematics, River Falls, WI 54022-5001
 Format: LaTeX MathJax PDF

## Abstract

We study the complementation of the space $W(X,Y)$ of weakly compact operators, the space $K(X,Y)$ of compact operators, the space $U(X,Y)$ of unconditionally converging operators, and the space $CC(X,Y)$ of completely continuous operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$. Feder proved that if $X$ is infinite-dimensional and $c_0 \hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Emmanuele and John showed that if $c_0 \hookrightarrow K(X,Y)$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Bator and Lewis showed that if $X$ is not a Grothendieck space and $c_0 \hookrightarrow Y$, then $W(X,Y)$ is uncomplemented in $L(X,Y)$. In this paper, classical results of Kalton and separably determined operator ideals with property $(*)$ are used to obtain complementation results that yield these theorems as corollaries.
 Keywords: spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operators
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]

 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2015 : https://cms.math.ca/