It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.
|Number of pages||22|
|Journal||Integral Equations and Operator Theory|
|Publication status||Published - May 2009|
ASJC Scopus subject areas
- Algebra and Number Theory