Backward Shifts on Banach SpacesC(X)
Copyright policy )Backward Shifts on Banach SpacesC(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 \(C(X)\).
- Cleveland State University United States
- University System of Ohio United States
- Tennessee State University United States
backward shift, one-dimensional kernel, Applied Mathematics, Classical Banach spaces in the general theory, Analysis, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
backward shift, one-dimensional kernel, Applied Mathematics, Classical Banach spaces in the general theory, Analysis, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
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