Norm-one projections in Banach spaces (Q5935718)

The paper is survey of results about norm-one projections and 1-complemented subspaces in K\(\ddot{o}\)the function spaces and Banach sequence spaces. The historical development of the theory is presented from the 1930s to the newest ideas. The survey starts with recalling well-known facts about abundance of contractive projections in Hilbert spaces and the characterizations of Hilbert spaces through existence of enough contractive projections. NEWLINENEWLINENEWLINEThe survey consists of two parts. Part I deals with nonatomic function spaces and Part II does with sequence spaces. Each part starts with the section devoted to the spaces \(L_p\) and \(\ell_p\), respectively. Also a variety of partial results valid in K\(\ddot{o}\)the function spaces and in sequence spaces. Besides proofs of the main results are outlined. Open problems are also discussed. The bibliography is pretty complete.