Let
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode"> be
the algebra of all bounded linear operators on a complex Banach space
X. We describe surjective linear maps
ϕ on
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode"> that satisfy
class="formula" id="fm0010">
class="mathml">
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si2.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=310ebd19c92fc17a918fe71dd86451d0" title="Click to view the MathML source">rϕ(T)(x)=0⟹rT(x)=0class="mathContainer hidden">class="mathCode">class="temp" src="/sd/blank.gif">
for every
class="mathmlsrc">class="formulatext stixSupport mathImg" 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∈Xclass="mathContainer hidden">class="mathCode"> and
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode">. We also describe surjective linear maps
ϕ on
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode"> that satisfy
class="formula" id="fm0020">
class="mathml">
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002437951630461X&_mathId=si5.gif&_user=111111111&_pii=S002437951630461X&_rdoc=1&_issn=00243795&md5=af342ea7f04fae036eecd0da682eef7c" title="Click to view the MathML source">rT(x)=0⟹rϕ(T)(x)=0class="mathContainer hidden">class="mathCode">class="temp" src="/sd/blank.gif">
for every
class="mathmlsrc">class="formulatext stixSupport mathImg" 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∈Xclass="mathContainer hidden">class="mathCode"> and
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode">. Fur
thermore, we characterize maps
ϕ (not necessarily linear nor surjective) on
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode"> which satisfy
class="formula" id="fm0030">
for every
class="mathmlsrc">class="formulatext stixSupport mathImg" 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∈Xclass="mathContainer hidden">class="mathCode"> and
class="mathmlsrc">class="formulatext stixSupport mathImg" 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)class="mathContainer hidden">class="mathCode">.