Rajagopalan, M.; Sundaresan, K. Backward shifts on Banach spaces \(C(X)\). (English) Zbl 0878.47014 J. Math. Anal. Appl. 202, No. 2, 485-491 (1996). 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 \(C(X)\). Reviewer: J.B.Cooper (Linz) Cited in 2 ReviewsCited in 8 Documents MSC: 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46B25 Classical Banach spaces in the general theory Keywords:backward shift; one-dimensional kernel PDFBibTeX XMLCite \textit{M. Rajagopalan} and \textit{K. Sundaresan}, J. Math. Anal. Appl. 202, No. 2, 485--491 (1996; Zbl 0878.47014) Full Text: DOI