Isometric and Almost Isometric Operators of B(L^1→L^1)

0.Introduetion As early ao in 1966,the following result wao aehievedby the ullons funotionalanalysio A.Pel,czyn,skia E.Miohael:ifo1,thenfo:evey

ISOMETRIC APPROXIMATION FROM 2-DIM BANACH SPACE INTO L^1[0,1]

In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Spacewhose unit ball is the union of a polygon C and the region enclosd by C in the plane. Also,the answer for IAP(Isometric Approximation Problem) on B(E2,L1 [0, 1]) is obtained.

Asymptotically Isometric Copy of l~β(0<β<1) in Spacesof Bounded Linear Operators

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.