Backward shifts on Banach spaces \(C(X)\)
A backward shift on a Banach space \(E\) is an operator \(T\) with one-dimensional kernel such that the corresponding operator from the quotient of \(E\) by the kernel of \(T\) is an isometry and so that \(\bigcup_{n\geq 1}\text{Ker }T^n\) is dense in \(E\). The authors settle a conjecture of J. R. Holub (in a stronger form) by proving that for no infinite compact space \(X\) is there a backward shift on \(C(X)\).
scientific article; zbMATH DE number 930204