On positive embeddings of C(K) spaces

• Autorzy: Grzegorz Plebanek
• Języki publikacji: EN

Abstrakty

EN

We investigate isomorphic embeddings T: C(K) → C(L) between Banach spaces of continuous functions. We show that if such an embedding T is a positive operator then K is the image of L under an upper semicontinuous set-function having finite values. Moreover we show that K has a π-base of sets whose closures are continuous images of compact subspaces of L. Our results imply in particular that if C(K) can be positively embedded into C(L) then some topological properties of L, such as countable tightness or Fréchetness, are inherited by K.
We show that some isomorphic embeddings C(K) → C(L) can be, in a sense, reduced to positive embeddings.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 216
• Numer: 2
• Strony: 179-192

Daty

wydano

2013

Twórcy

autor

Grzegorz Plebanek

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm216-2-5