Let
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) be the al
gebra of all bounded linear operators on a complex Banach space
X. We describe surjective linear maps
ϕ on
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) that satisfy
for every
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si31.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=38cc490618cfd493b4bd335f84309015" title="Click to view the MathML source">T∈L(X). We also describe surjective linear maps
ϕ on
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) that satisfy
for every
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si31.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=38cc490618cfd493b4bd335f84309015" title="Click to view the MathML source">T∈L(X). Furthermore, we characterize maps
ϕ (not necessarily linear nor surjective) on
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si1.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=8041826c7d2824d2f00de7e0dc6f9c83" title="Click to view the MathML source">L(X) which satisfy
for every
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si141.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=101de80a5bf6f8136a953e91f47a14f0" title="Click to view the MathML source">x∈X and
g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si148.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=af4fa2de0891bade88db17bf407ac2ea" title="Click to view the MathML source">T,S∈L(X).