Linear continuous surjections of Cp-spaces over compacta Academic Article uri icon

abstract

  • Abstract Let X and Y be compact Hausdorff spaces and suppose that there exists a linear continuous surjection T: C p (X)→ C p (Y), where C p (X) denotes the space of all real- valued continuous functions on X endowed with the pointwise convergence topology. We prove that dim⁡ X= 0 implies dim⁡ Y= 0. This generalizes a previous theorem [7, Theorem 3.4] for compact metrizable spaces. Also we point out that the function space C p (P) over the pseudo-arc P admits no densely defined linear continuous operator C p (P)→ C p ([0, 1]) with a dense image.

publication date

  • January 1, 2017