SIMULTANEOUS LIFTING THEOREM FOR BLOCK DIAGONAL OPERATORS Academic Article

Stampfli has shown that for a given T B ( H ) T, in ,Bleft ( H
ight ) there exists a K C ( H ) K, in ,Cleft ( H
ight ) so that ( T + K ) = w ( T ) sigma left ( {T, + , K}
ight ),= ,{sigma _w}left ( T
ight ) . An analogous result holds for the essential numerical range W e ( T ) {W_e}left ( T
ight ) . A compact operator K is said to preserve the Weyl spectrum and essential numerical range of an operator T B ( H ) T, in ,Bleft ( H
ight ) if ( T + K ) = w ( T ) sigma left ( {T, + , K}
ight ), = ,{sigma _w}left ( T
ight ) and W ( T +

authors

• Ward, Joseph